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	Model theory - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-17)
		In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the models which underlie mathematical systems.
		In the context of proof theory the analogous statement is trivial, since every proof can have only a finite number of antecedents used in the proof; in the context of model theory, however, this proof is somewhat more difficult.
		Model theory is usually concerned with first order logic, and many important results (such as the completeness and compactness theorems) fail in second order logic or other alternatives.
	www.bexley.us /project/wikipedia/index.php/Model_theory (860 words)

	Introduction
		Model theory is the study of the interpretations of any language, formal or natural, by means of set-theoretic or category-theoretic structures.
		First-order model theory is the branch of mathematics that deals with the relationships between descriptions in first-order languages and the structures that satisfy these descriptions.
		In support of the IFF Model Theory Ontology are the two lower levels of this structure, which are represented by the IFF Lower Classification Ontology (middle level) and the IFF Lower Core Ontology (lower level).
	suo.ieee.org /IFF/versions/20020515/IFFModelTheoryOntology/Introduction.htm (373 words)

	INI Programme MAA
		Model theory is a branch of mathematical logic dealing with abstract structures (models), historically with connections to other areas of mathematics.
		In the past decade, model theory has reached a new maturity, allowing for a strengthening of these connections and striking applications to diophantine geometry, analytic geometry and Lie theory, as well as strong interactions with group theory, representation theory of finite-dimensional algebras, and the study of the p-adics.
		Applied model theory on the other hand studies concrete algebraic structures from a model-theoretic point of view, and uses results from pure model theory to get a better understanding of the structures in question, of the lattice of definable sets, and of various functorialities and uniformities of definition.
	www.newton.cam.ac.uk /programmes/MAA (445 words)

	Model Theory: An Introduction
		Model theory is a branch of mathematical logic where we study mathematical structures by considering the first-order sentences true in those structures and the sets definable by first-order formulas.
		My goal was to write an introductory text in model theory that, in addition to developing the basic material, illustrates the abstract and applied directions of the subject and the interaction of these two programs.
		The methods of Sections 4.2 and 4.3 are used to study countable models in Section 4.4, where we examine $\aleph_0$-categorical theories and prove Morley's result on the number of countable models.
	www.math.uic.edu /~marker/mt-intro.html (1958 words)

	Model Theory
		Model theory began with the study of formal languages and their interpretations, and of the kinds of classification that a particular formal language can make.
		But in a broader sense, model theory is the study of the interpretation of any language, formal or natural, by means of set-theoretic structures, with Alfred Tarski's truth definition as a paradigm.
		These are very different senses of ‘model’ from that in model theory: the ‘model’ of the phenomenon or the system is not a structure but a theory, often in a formal language.
	plato.stanford.edu /entries/model-theory (6225 words)

	RDF Model Theory
		precise semantic theory for RDF and RDFS, and to sharpen the notions of consequence and inference.
		The model theory assigns interpretations directly to the graph; we will refer to this as the 'graph syntax' to avoid ambiguity, since the bare term 'syntax' is often assumed to refer to a lexicalization.
		To apply the model theory to this kind of situation, one should think of the assertion of such a graph as amounting to an assertion of the merge of that graph together with whatever RDF graphs are assumed to define the public vocabulary, in order to fully convey the intended meaning of the 'public' assertion.
	www.w3.org /TR/2002/WD-rdf-mt-20020429 (11311 words)

	Overview of Logic (Site not responding. Last check: 2007-10-17)
		The study of formal systems naturally separates into two areas, proof theory which is concerned with language, axioms, inference, and what is provable and model theory which is concerned with the relationship between the structure and the language and whether what is true is provable.
		Thus, model theory begins with a class of set-theoretic objects called relational structures and constructs a language and a mapping from the language to the structure.
		A theory T is said to be incomplete, if for some formula f, T=f but it is not the case that T -f i.e., some formula is true but is not a theorem.
	cs.wwc.edu /~aabyan/Logic/Overview.html (4089 words)

	The Mathematics of Boolean Algebra
		The study of Boolean algebras has several aspects: structure theory, model theory of Boolean algebras, decidability and undecidability questions for the class of Boolean algebras, and the indicated applications.
		These two processes are inverses of one another, and show that the theory of Boolean algebras and of rings with identity in which every element is idempotent are definitionally equivalent.
		Much of the deeper theory of Boolean algebras, telling about their structure and classification, can be formulated in terms of certain functions defined for all Boolean algebras, with infinite cardinals as values.
	setis.library.usyd.edu.au /stanford/entries/boolalg-math (2054 words)

	Semantic Web Model Theory (Site not responding. Last check: 2007-10-17)
		Model theory is usually most relevant to implementation via the notion of entailment, described later, and by making it possible to define valid inference rules.
		One approach is for each of the SWEL to use their own model theory, layering it on top of the model theories of the languages they are layered upon.
		A structure is an idealized view of the world, simply construed as a set of individuals with relations between them.
	tap.stanford.edu /sw/swmt.html (1923 words)

	RDF Semantics (Site not responding. Last check: 2007-10-17)
		model theory for specifying the semantics of a formal language.
		Readers unfamiliar with model theory may find the glossary in appendix B helpful; throughout the text, uses of terms in a technical sense are linked to their glossary definitions.
		An alternative way to specify a semantics is to give a translation from RDF into a formal logic with a model theory already attached, as it were.
	www.w3.org /TR/rdf-mt (11716 words)

	Downloading "Fundamentals of Model Theory" (Site not responding. Last check: 2007-10-17)
		Model Theory is the part of mathematics which shows how to apply logic to the study of structures in pure mathematics.
		This book provides an introduction to Model Theory which can be used as a text for a reading course or a summer project at the senior undergraduate or graduate level.
		More importantly, the methods of Model Theory display clearly the structure of the main ideas of the proofs, showing how theorems of logic combine with theorems from other areas of mathematics to produce stunning results.
	www.math.toronto.edu /weiss/model_theory.html (635 words)

	The Bohr Model
		The Bohr Model is probably familar as the "planetary model" of the atom illustrated in the adjacent figure that, for example, is used as a symbol for atomic energy (a bit of a misnomer, since the energy in "atomic energy" is actually the energy of the nucleus, rather than the entire atom).
		In the Bohr Model the neutrons and protons (symbolized by red and blue balls in the adjacent image) occupy a dense central region called the nucleus, and the electrons orbit the nucleus much like planets orbiting the Sun (but the orbits are not confined to a plane as is approximately true in the Solar System).
		This similarity between a planetary model and the Bohr Model of the atom ultimately arises because the attractive gravitational force in a solar system and the attractive Coulomb (electrical) force between the positively charged nucleus and the negatively charged electrons in an atom are mathematically of the same form.
	csep10.phys.utk.edu /astr162/lect/light/bohr.html (711 words)

	Logical Consequence, Model-Theoretic Conceptions [Internet Encyclopedia of Philosophy]
		A model for a language L is the theoretical development of a possible interpretation of non-logical terminology of L according to which the sentences of L receive a truth-value.
		The intended structure for a language L is the course-grained representation of the piece of the world that we intend L to be about.
		They are central questions in the philosophy of logic and their significance is at least partly due to the prevalent use of model theory in logic to represent logical consequence in a variety of languages.
	www.iep.utm.edu /l/logcon-m.htm (9582 words)

	Model Theory and Spirituality
		A 3-dimensional hologram of a complex neural structure, surrounding that structure, energized by a repetitive energy wave, would repetitively excite the shape of that neural structure.
		Yet some experimentation has shown that parts of this model seem to be shared by others; thus, personal responsibility is prudent regarding modifications to what appears to be just one's own model.
		A model of one's ongoing life experience might be represented by a set of four overlays.
	home.earthlink.net /~jedcline/mdlthry.html (2183 words)

	Semantic Web Model Theory (Site not responding. Last check: 2007-10-17)
		One approach is for each of the SWELs to be defined in terms of their own model theory, layering it on top of the model theories of the languages they are layered upon.
		The model theory also has nothing to say about whether a uri such as "http://www.w3.org/" denotes the World Wide Web Consortium or the HTML page accessible at that URI or the web site accessible via that URI.
		The important point to note about the avove diagram is that if the Li to Lbase mapping and model theory for Li are done consistently, the Li model theory interpretations satisfying G will be the same as the Lbase model theory interpretations satisfying G (modulo the richer interpretations not in Li's MT).
	tap.stanford.edu /SemanticWebSemantics.html (3132 words)

	RDF Model Theory
		The model theory assigns interpretations directly to the graph, which is taken as being the primary RDF syntax, in the sense that two RDF documents, in whatever lexical form, are syntactically equivalent if and only if they map to the same RDF graph.
		As stated here, the model theory only supports interpretations in which containers are 'opaque' objects, so that assertions involving containers are about those containers, rather than being understood 'transparently' to be asserting anything about the members of the containers.
		With the current model theory, this says that the value of foo is baz for some thing in the Alt container, which might be aaa, bbb or something else not mentioned in the graph.
	blogspace.com /rdf/modeltheory (4775 words)

	Basic Model Theory
		Model theory investigates the relationships between mathematical structures (models) on the one hand and formal languages (in which statements about these structures can be formulated) on the other.
		Examples of these structures are the natural numbers with the usual arithmetical operations; the structures familiar from algebra; and ordered sets.
		An example of a result is Lowenheim's theorem (the oldest in the field): a first-order sentence true of some uncountable structure must hold in some countable structure as well.
	www.allbookstores.com /book/1575860481 (212 words)

	Model Theory. Goedel's Completeness Theorem. Skolem's Paradox. Ramsey's Theorem. By K.Podnieks
		Model theory is investigation of formal theories in the metatheory ZFC.
		They thought that mere consistency of a theory (in the syntactic sense of the word - as the lack of contradictions) is not sufficient to regard a theory as a "meaningful" one.
		Model Existence Theorem says that (syntactic!) consistency of a theory is sufficient to regard it as "meaningful": if a theory does not contain contradictions, then it describes at least some kind of "mathematical reality".
	www.ltn.lv /~podnieks/gta.html (5980 words)

	Amazon.ca: Books: Model Theory (Site not responding. Last check: 2007-10-17)
		This book was for a while the classic text in model theory, and it still is a good resource for a student in the area.
		This was the first model theory text I read, and I've always found the proofs to be clear, straightforward, and easy to read.
		For instance, in 1978 Shelah wrote a famous book that simultaneously answered many open questions in model theory and changed the direction of the whole subject, and the 1990's have seen many new applications to algebra and other areas of pure math.
	www.amazon.ca /exec/obidos/ASIN/0444880542 (869 words)

	Instructional Design Models
		An instructional design model gives structure and meaning to an I.D. problem, enabling the would-be designer to negotiate her design task with a semblance of conscious understanding.
		The value of a specific model is determined within the context of use.
		A model should be judged by how it mediates the designer's intention, how well it can share a work load, and how effectively it shifts focus away from itself toward the object of the design activity.
	carbon.cudenver.edu /~mryder/itc_data/idmodels.html (1202 words)

	Symplectic geometry seminar (Site not responding. Last check: 2007-10-17)
		Abstract: An almost complex manifold is a manifold M with a complex structure J on the fibers of the tangent bundle TM.
		We explore the geometry of almost complex manifolds by means of model theory.
		In model theory, a "structure" is an infinite set D together with a collection of subsets of D^n closed under intersections, complements, projections and their inverses, and containing the diagonals.
	www.math.toronto.edu /symplec/fall02/sem120202.html (153 words)

	Analyzing the logical structure of relativity theory via model theoretic (Site not responding. Last check: 2007-10-17)
		This is a lecture notes for a course given March 1 - April 20, 1998 in CCSOM of the University of Amsterdam.
		Our version of relativity theory will consist of a small number of axioms which are not only in first order logic, but are moreover easily comprehensible.
		the logical structure of the theory, the number of non-elementarily-equivalent models, classification of models, etc. Among other things, we will use logic to find out which axioms are responsible for certain surprising predictions of relativity theory like e.g.
	www.math-inst.hu /pub/algebraic-logic/relativity.html (587 words)

	Fields Institute - Algebraic Model Theory Program
		We will see that tame congruence theory provides a means to analyze the local structure of finite algebras and also to obtain useful information about the varieties they generate.
		We will examine the structure of varieties whose first order theories are recursive (decidable varieties) and in particular will discuss the results of McKenzie-Valeriote and Idziak-Jeong.
		Tame congruence theory has turned out to be a useful tool in trying to understand the residual character of varieties.
	www.fields.utoronto.ca /programs/scientific/96-97/algebraic/algebra-course.html (204 words)

	FSTTCS 98 - School on Finite Model Theory (Site not responding. Last check: 2007-10-17)
		Finite model theory is concerned with the study of various logical languages over classes of finite structures.
		This area has some affinity with classical model theory but has developed a distinct identity, both in terms of the questions considered and the techniques used.
		The questions it is concerned with are motivated by connections with computation, and it has developed a variety of logics and new techniques for studying their expressive power over finite structures.
	www.imsc.ernet.in /~fsttcs98/fmt.html (245 words)

	[SCL] Simplified SCL model theory presentation
		However, if some name is in fact ONLY used as a relation (in some piece of SCL text) and not as an individual name, then the MT should not require that it denote an individual in all interpretations of that text.
		C does not affect satisfiability but is still desireable, since there are meta-results in model theory which could be harmed by irrelevant clutter.
		This deals adequately with A and B but not with C. So to handle C, we have a notion of a 'pruned interpretation' which is a different kind of interpretation with all extraneous structure removed, ie what is here called 'folded'.
	grimpeur.tamu.edu /pipermail/scl/2004-May/000764.html (866 words)

	Allen 1995: Chapter 8 - Semantics and Logical Form (Site not responding. Last check: 2007-10-17)
		It describes a model theory for the logical form language and discusses various semantic relationships among sentences that can be defined in terms of entailment and implicature.
		Although this ambiguity does have semantic consequences, it is actually rooted in the syntactic structure; that is, whether the conjunction involves two noun phrases, (Happy cats) and (dogs), or the single noun phrase (Happy (cats and dogs)).
		The syntactic structures of these sentences are identical, but different senses of the verb run must be selected because of the possible senses in the modifier.
	www.uni-giessen.de /~g91062/Seminare/gk-cl/Allen95/al199508.htm (9268 words)

	Fields Institute - Algebraic Model Theory Program
		In 1996-97 The Fields Institute for Research in Mathematical Sciences will be sponsoring an emphasis year in Algebraic Model Theory.
		There will be a NATO ASI on Algebraic Model Theory from August 19 to August 30 at The Fields Institute.
		March 17-21, Workshop on The Model Theory of Analytic Functions,
	www.fields.utoronto.ca /programs/scientific/96-97/algebraic (284 words)

	Semantics and Model theory (Site not responding. Last check: 2007-10-17)
		Chapter 7 contains more details about relational structures.
		is extended to mean that the formula f is true in all those structures in which the axioms of T are true.
		Chapter 6 contains more details about semantics and model theory.
	cs.wwc.edu /~aabyan/Logic/Book/book/node20.html (435 words)

	Completeness Theorems. Model Theory. Mathematical Logic. Part 4.
		His name is attached to objects in several fields of logic from Kripke-Platek axioms in higher recursion theory to the "Brouwer-Kripke scheme" in intuitionistic mathematics.
		Kripke models for modal logic, a discovery he made in his teen-age years, became part of the standard vocabulary of mathematical logicians after his first article appeared in 1963, when he was just 23 years old.
		Of course, our proof will be by induction along the structure of the formula F. a) F is an atomic formula.
	www.ltn.lv /%7Epodnieks/mlog/ml4a.htm (5408 words)

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