
	Where results make sense

Topic: Finitary

Related Topics

finitary operation

In the News (Mon 28 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Finitary - Wikipedia, the free encyclopedia
		In mathematics or logic, a finitary operation is one, like those of arithmetic, that take a number of input values to produce an output.
		A finitary argument is one which can be translated into a finite set of symbolic propositions starting from a finite set of axioms.
		The aim itself was proved impossible by Kurt Gödel in 1931, with his Incompleteness Theorem, but the general mathematical trend is to use a finitary approach, arguing that this avoids considering mathematical objects that cannot be fully defined.
	en.wikipedia.org /wiki/Finitary (522 words)

	Hilbert's program - Wikipedia, the free encyclopedia
		The question of whether there are finitary consistency proofs of strong theories is difficult to answer, mainly because there is no generally accepted definition of a "finitary proof".
		Most mathematicians in proof theory seem to regard finitary mathematics as being contained in Peano arithmetic, and in this case it is not possible to give finitary proofs of reasonably strong theories.
		On the other hand Godel himself suggested the possibility of giving finitary consistency proofs using finitary methods that cannot be formalized in Peano arithmetic, so he seems to have had a more liberal view of what finitary methods might be allowed.
	en.wikipedia.org /wiki/Hilbert's_program (894 words)

	Finitary Winning in \omega-Regular Games
		A stronger formulation of liveness, so-called finitary liveness, overcomes this drawback, while still retaining robustness and simplicity.
		Finitary liveness requires that there exists an unknown, fixed bound b such that something good happens within b transitions.
		While for one-shot liveness (reachability) objectives, classical and finitary liveness coincide, for repeated liveness (BÃ¼chi) objectives, the finitary formulation is strictly stronger.
	chess.eecs.berkeley.edu /pubs/82.html (284 words)

	Hilbert's Program
		For the same reason, a finitary general proposition is not to be understood as an infinite conjunction but "only as a hypothetical judgment that comes to assert something when a numeral is given" (ibid.).
		Contentual induction was accepted in its application to finitary statements of the hypothetical, general kind explicitly in Hilbert (1922b).
		Since finitary reasoning is that part of mathematics which is presupposed by all non-trivial reasoning about numbers, it is, so Tait, "indubitable" in a Cartesian sense, and this indubitability as all that would be required of finitary reasoning to provide the epistemological grounding of mathematics Hilbert intended it for.
	plato.stanford.edu /entries/hilbert-program (7511 words)

	Alur/Henzinger: Finitary Fairness (Site not responding. Last check: 2007-10-31)
		We argue that the standard definition of fairness often is unnecessarily weak and can be replaced by the stronger, yet still abstract, notion of finitary fairness.
		While standard weak fairness requires that no enabled transition is postponed forever, finitary weak fairness requires that for every run of a system there is an unknown bound k such that no enabled transition is postponed more than k consecutive times.
		In general, the finitary restriction fin(F) of any given fairness assumption F is the union of all omega-regular safety properties that are contained in F.
	www.cis.upenn.edu /~alur/Lics94.html (244 words)

	On the Finitary Bisimulation (Site not responding. Last check: 2007-10-31)
		The finitely observable, or finitary, part of bisimulation is a key tool in establishing full abstraction results for denotational semantics for process algebras with respect to bisimulation-based preorders.
		A bisimulation-like characterization of this relation for arbitrary transition systems is given, relying on Abramsky's characterization in terms of the finitary domain logic.
		More informative behavioural, observation-independent characterizations of the finitary bisimulation are also offered for several interesting classes of transition systems.
	www.brics.dk /RS/95/59/index.html (111 words)

	PhilSci Archive - Quantum superposition principle justified in a new non-Aristotelian finitary logic
		Quantum superposition principle justified in a new non-Aristotelian finitary logic
		In the proposed non-Aristotelian finitary logic (NAFL), truths for formal propositions can exist only with respect to axiomatic theories, essentially as temporary axiomatic declarations in the human mind.
		Here T* is an axiomatic NAFL theory that, like T, resides in the human mind and acts as the "truth-maker" for (a model of) T. Quantum superposition is justified by identifying "axiomatic declarations" for the truth/falsity of $P$ (by virtue of its provability/refutability in T*) with "measurement" in the real world.
	philsci-archive.pitt.edu /archive/00001923 (268 words)

	BIALYSTOK UNIV. PL * MATHESIS UNIVERSALIS, No.7, 1998 * W.Marciszewski: Post's Problem of Creativity
		Post contributed to grasping the essence of finitary mechanical operations on equal footing with Turing and Hilbert.
		However, it seems to the writer that logic should be considered essentially a human enterprise, and that when this is departed from, it is then incumbent on such a writer to add a qualifying ``non-finitary''.
		Whatever this should mean, there arises the question concerning a source of that capability of `seeing the infinitude' which transdends the abilities of a machine.
	www.calculemus.org /MathUniversalis/7/09marci.html (3126 words)

	Mislove N00014-91-J-1692
		Last year, we reported on an extension of this result that showed that recursion operators can be added to the finitary sublanguage, again assuming some conditions on the models of the finitary sublanguage with which one begins.
		The results just described applied to any finitary language (i.e., they do not assume the language is a free or an initial algebra), but the model for the language of closed terms produced by the theory does not satisfy any equations, even if the original language satisfied them.
		For example, even if the sequential composition operation ";" in the denotational model for the finitary model were assumed to be associative, the same would not be true of this operation in the denotational model for the language of closed terms.
	www.math.tulane.edu /~mwm/ftp/eoyl95.html (2603 words)

	PhilSci Archive - Quantum superposition justified in a new non-Aristotelian finitary logic
		Quantum superposition principle justified in a new non-Aristotelian finitary logic (deposited 01 September 2004)
		Quantum superposition justified in a new non-Aristotelian finitary logic.
		Platonism in classical logic versus formalism in the proposed non-Aristotelian finitary logic.
	philsci-archive.pitt.edu /archive/00000635 (246 words)

	PDMI Preprint 06/2000 (Site not responding. Last check: 2007-10-31)
		A sketch of a finitary version of mathematical analysis.
		Finitary completions of elementary metric and countably metric spaces as finitary counterparts of function spaces of classical mathematics.- 5.
		On the theorems of finitary mathematics that have the form of majorants of theorems of `broad' constructive mathematics.- Appendices.- Bibliography.
	www.pdmi.ras.ru:8101 /preprint/2000/00-06.html (107 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		Finitary automorphism groups over non-commutative rings, J. London Math.
		Finitary linear images of finitary linear groups, Math.
		On the countable recognition of finitary groups, J. London Math.
	www.maths.qmw.ac.uk /~bafw/pubs.html (228 words)

	LC '98 abstract: Sergei Tupailo (Site not responding. Last check: 2007-10-31)
		But most recently, there has been an interest to what one can get on the side of finitary proof theory from the methods which are used for proof-theoretical analysis of impredicative theories.
		Cutelimination for the finitary system formally makes no reference to its infinitary version, reduction steps being defined by primitive recursion on the derivation.
		Finitary reductions for local predicativity, I: recursively regular ordinals.
	www.math.cas.cz /~lc98/abstracts/Tupailo.html (424 words)

	Finitary Approximations and Metric Structure of the Space of Clones
		Finitary Approximations and Metric Structure of the Space of Clones
		In order to get a better perspective on L/sub k/, we firstly propose to define finitary approximation of L/sub k/, which is some simplified structure of L/sub k/.
		Citation: H. Machida, "Finitary Approximations and Metric Structure of the Space of Clones," ismvl, p.
	csdl.computer.org /comp/proceedings/ismvl/1995/7118/00/71180200abs.htm (282 words)

	On the Existence and Non-existence of Finitary Codings for a Class of Random Fields
		On the Existence and Non-existence of Finitary Codings for a Class of Random Fields
		We study the existence of finitary codings (also called finitary homomorphisms or finitary factor maps) from a finite-valued i.i.d.
		For Markov random fields we show, using ideas of Marton and Shields, that the presence of a phase transition is an obstruction for the existence of the above coding: this yields a large class of Bernoulli shifts for which no such coding exists.
	research.microsoft.com /research/pubs/view.aspx?pubid=499 (172 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		There are two main approaches to ordinal analysis of formal theories: the finitary Gentzen-Takeuti approach on the one side, and the use of infinitary derivations initiated by Schuette on the other.
		In a series of two talks we will show how translating infinitary proof theory into the finitary one can be done for the method of local predicativity.
		It should be noted that our procedure is closed to W. Pohlers' original presentation of the method, but not to the method of 'operator-controlled derivations' introduced later by W. Buchholz.
	www-philosophy.stanford.edu /Logic/Abstracts/Seminar/021798 (438 words)

	FLoC '02 - ICLP Thursday August 1st
		For all finitary programs, ground goals are decidable, while nonground goals are semidecidable.
		Moreover, the existing engines (that currently accept only much more restricted programs) can be extended to handle finitary programs by replacing their front-ends and keeping their core inference mechanism unchanged.
		More precisely, we introduce a suitable generalization of the notion of finitary program and extend all the results of the authors previous work to this class.
	floc02.diku.dk /ICLP/Thursday.html (1270 words)

	Part 3: A Very Very Very Very Very Very Pathetic and Ignorant Book (Site not responding. Last check: 2007-10-31)
		The particular theory that they adopted was first-order predicate logic with a finitary proof theory.
		By "safe logical principles", Kline is referring to first-order logic and finitary proof theory, which was regarded as "safe" by the classical formalists.
		For this purpose, Hilbert initiated metamathematics and the finitary standpoint...Let S be any consistent formal system containing the theory of natural numbers.
	www.mathpages.com /home/kmath347/kmvs03.htm (965 words)

	Proceedings of the American Mathematical Society
		Abstract: We give two applications of the recent classification of locally finite simple finitary skew linear groups.
		We show that certain irreducible finitary skew linear groups of infinite dimension generate the variety of all groups and have infinite Prüfer rank.
		P., `The lawlessness of groups of finitary permutations', Arch.
	www.ams.org /proc/2002-130-10/S0002-9939-02-06673-X/home.html (259 words)

	Citebase - Finitary Spacetime Sheaves (Site not responding. Last check: 2007-10-31)
		The notion of finitary spacetime sheaves is introduced based on locally finite approximations of the continuous topology of a bounded region of a spacetime manifold.
		Finitary spacetime sheaves are seen to be sound mathematical models of approximations of continuous spacetime observables.
		Users are cautioned not to use it for academic evaluation yet.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:gr-qc/0102108 (94 words)

	A Finitary Treatment of the Closed Fragment of Japaridze's Provability Logic -- Beklemishev et al. 15 (4): 447 -- ...
		A Finitary Treatment of the Closed Fragment of Japaridze's Provability Logic -- Beklemishev et al.
		A Finitary Treatment of the Closed Fragment of Japaridze's Provability Logic
		by purely finitary means formalizable in elementary arithmetic.
	logcom.oxfordjournals.org /cgi/content/short/15/4/447?rss=1 (256 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		Sergei Tupailo Finitary reductions for local predicativity, II: recursively Mahlo ordinals We will present a method of extracting finitary reductions for a theory stating existence of recursively Mahlo ordinals.
		The method is the same as for a theory of strength of ID_1, presented at this seminar last quarter (see http://www-logic.stanford.edu/Abstracts/Seminar/021798), but of course presence of Mahlo makes proof-theoretical analysis itself (by either infinitary or finitary approach) more involved.
		Since extracting finitary reductions follows completely standard method and was presented by G. Mints at last seminar and ourselves on February 24 in some detail, we will not talk much about it but only outline some general features involved there.
	www-logic.stanford.edu /Abstracts/Seminar/051998 (119 words)

	Atlas: On Finitary Interpretations of Theorems of the Theory of Algorithms and Recursively Enumerable Sets by Nikolai ... (Site not responding. Last check: 2007-10-31)
		The statements of theorems of the theory of algorithms and recursively enumerable sets (including some basic theorems) often go beyond the limits of languages of finitary mathematics thus being "semantic riddles" (from the point of view of the finitary mathematical thought).
		For a series of such theorems (including undecidability of several mass problems), finitarily sensible and finitarily provable strengthenings (finitary majorants) are introduced.
		They are usually extracted from the "natural" procedures of deduction of the theorems by means of wider constructive mathematics while at the same time suiting the role of finitary versions of our non-finitary statements.
	atlas-conferences.com /cgi-bin/abstract/cajy-22 (185 words)

	Infinitary Logic
		In the course of the discussion it will be seen that, while the expressive power of such languages far exceeds that of their finitary (first-order) counterparts, very few of them possess the "attractive" features (e.g., compactness and completeness) of the latter.
		Given a pair κ, λ of infinite cardinals such that λ ≤ κ, we define a class of infinitary languages in each of which we may form conjunctions and disjunctions of sets of formulas of cardinality < κ, and quantifications over sequences of variables of length < λ.
		— the (finitary) base language — be an arbitrary but fixed first-order language with any number of extralogical symbols.
	plato.stanford.edu /entries/logic-infinitary (6663 words)

	Problems
		In the case of finitary PCF, it is sufficient to restrict the language to exclude fixed point operations, but include
		For instance, assuming 3(ii), given a type we can work our way along an enumeration of finitary-PCF terms till we have obtained as many distinct functions as given by the algorithm for 3(iii), and thus obtain (2).
		One can ask the questions asked of finitary PCF for the variant where instead of beginning the hierarchy as booleans with
	www.brics.dk /FA/Problems/FA-Problems/FA-Problems.html (348 words)

	Emrah YAKA (Site not responding. Last check: 2007-10-31)
		In this thesis, we studied two different subjects, namely, groups with permuting with finitely many of its conjugates and groups of finitary permutations.
		In the first part of the thesis, we made a survey of some results of V.E. Kislyakov about groups with an element a permuting with finitely many of its conjugates.
		In the second part of the thesis, we made a survey of some results of P.M. Neumann about the transitive finitary permutation groups.
	www.math.metu.edu.tr /academic/yaka_emrah.html (231 words)

	Citebase - Finitary Topos for Locally Finite, Causal and Quantal Vacuum Einstein Gravity (Site not responding. Last check: 2007-10-31)
		Finitary Topos for Locally Finite, Causal and Quantal Vacuum Einstein Gravity
		This topos is seen to be a finitary instance of both an elementary and a Grothendieck topos, generalizing in a differential geometric setting, as befits ADG, Sorkin's finitary substitutes of continuous spacetime topologies.
		The paper closes with a thorough discussion of four future routes we could take in order to further develop our topos-theoretic perspective on ADG-gravity along certain categorical trends in current quantum gravity research.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:gr-qc/0507100 (161 words)

Try your search on: Qwika (all wikis)