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Topic: Forcing mathematics

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	Forcing (mathematics) - Wikipedia, the free encyclopedia
		Forcing was considerably reworked and simplified in the sixties, and is nowadays a basic technique.
		Forcing is equivalent to the method of Boolean-valued models, which is conceptually more natural and intuitive, but usually much more difficult to apply.
		Forcing is a more elaborate version of this idea, reducing the expansion to the existence of one new set, and allowing for fine control over the properties of the expanded universe.
	en.wikipedia.org /wiki/Forcing_(mathematics) (2954 words)

	Forcing (mathematics) -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		Forcing was considerably reworked and simplified in the (The time of life between 60 and 70) sixties, and is nowadays a basic technique.
		To reduce the study of the set theory of M[G] to that of M, one works with the forcing language, which is built up like ordinary (Click link for more info and facts about first-order logic) first-order logic, with membership as binary relation and all the names as constants.
		In forcing we usually seek to show some sentence is consistent with (Click link for more info and facts about ZFC) ZFC (or optionally some extension of ZFC).
	www.absoluteastronomy.com /encyclopedia/f/fo/forcing_(mathematics).htm (3103 words)

	[No title]
		Forcing, as we shall see later, comes in when one tries to prove that M[G] satisfies various statements (or, in the usual jargon, that various statements are "true in M[G]").
		Forcing is needed to prove the Fundamental Theorem, since we have to prove that each axiom of ZFC is true in M[G].
		Forcing is also needed to prove that ~CH is true in M[G] (for a suitable G).
	www-math.mit.edu /~tchow/mathstuff/forcingdum (4040 words)

	Model theory
		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.
		It assumes that there are some pre-existing mathematical objects out there, and asks questions regarding how or what can be proven given the objects, some operations or relations amongst the objects, and a set of axioms.
		The independence of the axiom of choice and the continuum hypothesis from the other axioms of set theory (proven by Paul Cohen and Kurt Gödel) are the two most famous results arising from model theory.
	www.brainyencyclopedia.com /encyclopedia/m/mo/model_theory.html (828 words)

	Mathematica Programmed Interactive Animations (Site not responding. Last check: 2007-10-21)
		Forced oscillations on coupled masses are treated similarly to the one degree of freedom vibration problems.
		In Mathematics Departments where some academic staff are not "plugged-in" to Science and Technology, lecturers may use a language that is not that meaningful to Engineering students or even to the rest of the non-mathematical professional community.
		It may be argued that Mathematics is a precise language and this ought to be taught to the community.
	linus.socs.uts.edu.au /~bobr/IMM_Eigenvalues/IMAconf.html (2375 words)

	No Title
		I have been working on periodic forcing of spiral waves and three-dimensional scroll waves, both with numerical PDE models and in the case of spiral waves via an analysis of an ODE model given by the spiral symmetries.
		Having realized that in 2-D, there is no qualitative difference between a periodically forced rigidly rotating spiral and a meandering spiral (only the origin of the secondary rotation is different [1]), I decided to investigate the phenomenon of meander in three-dimensional scroll waves via periodic forcing.
		With resonant periodic forcing, it is possible to move a scroll wave locally in a direction normal to its filament.
	www.ima.umn.edu /~mantel/interest/interest.html (777 words)

	Nat' Academies Press, Measuring What Counts: A Conceptual Guide for Mathematics Assessment (1993)
		Rather than forcing mathematics to fit assessment, assessment must be tailored to whatever mathematics is important to learn.
		The mathematics in an assessment should never be distorted or trivialized for the convenience of assessment.
		In summary, rather than forcing mathematics to fit assessment, assessment must be tailored to whatever mathematics is important to assess.
	www.nap.edu /books/0309049814/html/62.html (542 words)

	Winfried Just's professional interests
		Currently, I work on applications of mathematics to biology, in particular, on game-theoretic models of animal interactions and on the multiple alignment problem which is of crucial importance in the new science of bioinformatics.
		The meaning of this somewhat pompous phrase is that all the structures studied in various branches of mathematics can be interpreted as sets, and hence all mathematical theorems can, at least in principle, be derived from the rules governing the formation of sets.
		A second force that drives recent developments in biomathematics is the unprecedented proliferation of biological data, especially genomic data.
	www.math.ohiou.edu /~just/resint.html (1601 words)

	Multiple Supercritical Solitary Wave Solutions of the Stationary Forced Korteweg-De Vries Equation and Their Stability
		The forcing represented by the function $f(x)$ in the fKdV equation is due to the bump on the bottom of the channel.
		An analytic expression of the SPSWS is found when the forcing is a rectangular bump or dent (called the well-shape forcing).
		Multiple SPSWS are also found numerically when the forcing is a partly negative and partly positive bump, and two semi-elliptic bumps, respectively.
	epubs.siam.org /sam-bin/dbq/article/23351 (311 words)

	Set Theory (Studies in Logic and the Foundations of Mathematics): Current Amazon U.S.A. One-Edition Data
		For instance, his treatment makes very clear how to define the forcing relation in the ground model; why inaccessibles can't be proven consistent with ZFC using ZFC alone; how transfinite recursion should be formally stated in the theory and how it is to be used formally; and what the different approaches to forcing are.
		The main topics in the book are constructibility (developed on the basis of an understanding of ordinal definability) and forcing, with a final chapter on iterated forcing.
		The last chapter on forcing is the big payoff of the book and has lots of exercises, but still a shortage of examples.
	www.mysqlwebhosting.biz /stuff-0444868399.html (751 words)

	The Higher Infinite : Large Cardinals in Set Theory from Their Beginnings (Springer Monographs in Mathematics): Current ...
		The theory of large cardinals is currently a broad mainstream of modern set theory, the main area of investigation for the analysis of the relative consistency of mathematical propositions and possible new axioms for mathematics.
		Forcing and sets of reals (introducing descriptive set theory and forcing in an excellent way).
		It is true that a future volume is promised in which "a wide range of forcing consistency results" will be presented, but it is also true that the book claims to have been written as a "genetic account through historical progression", and without much more forcing- well, this simply is not the case.
	www.mysqlwebhosting.biz /stuff-3540003843.html (936 words)

	Infinite Ink: The Continuum Hypothesis by Nancy McGough
		Under the influence of axiomatic and bookish traditions, man perceived in discontinuity the first mathematical Being: "God created the integers and the rest is the work of man." This maxim spoken by the algebraist Kronecker reveals more about his past as a banker who grew rich through monetary speculation than about his philosophical insight.
		Maybe a similar path should be taken in mathematics, away from thinking of point sets as the fundamental objects and towards thinking of structures and relations as the fundamental objects of mathematics.
		Since CH is not a standard assumption in mathematics and, in fact, most set theorists think it is false, it is important for a writer to state her assumptions about CH.
	ii.best.vwh.net /math/ch (4563 words)

	forcing - OneLook Dictionary Search
		Forcing : Eric Weisstein's World of Mathematics [home, info]
		Example: "A public force is necessary to give security to the rights of citizens"
		Phrases that include forcing: forcing out, radiative forcing, forcing functions, forcing mechanism, 1nt forcing, more...
	www.onelook.com /?w=forcing&ls=a (399 words)

	Student Pages: Brad Forrest
		Figure 1 is the plot of the neutral stability curves at low frequency, while Figure 2 is a plot of the neutral stability curves at high frequency.
		I also produced a short animation (in mpg and avi formats) that shows how these neutral stability curves change qualitatively as the non-dimensional forcing frequency is increased from 10^-10 to 10^5.
		For low forcing frequency, surface tension is the dominant effect, while for high forcing frequency surface tension is dominated by viscosity.
	www.math.hmc.edu /~ajb/students/forrest (727 words)

	[No title]
		In mathematical terms this non-computability often is an obstacle to obtain a quantitative stability analysis and rates of convergence.
		Woodin proved that $\Sigma^2_1$ statements are absolute for set forcing between models of "ZFC + CH + there are many large cardinals" (A $\Sigma^2_1$ statement is one which allows one existential quantification over sets of reals --- CH is a $\Sigma^2_1$ statement).
		On the other hand, ACFA is an example of a "generic structure." There are several ways to say what a generic structure is; one of them uses the model-theoretic forcing, a notion that somewhat resembles its set-theoretic counterpart.
	www.math.cmu.edu /~rami/seminar.past.html (4515 words)

	Model theory Article, Modeltheory Information
		In mathematics, model theory is the study of therepresentation of mathematical concepts in terms of set theory, or the study ofthe models which underlie mathematical systems.
		It assumesthat there are some pre-existing mathematical objects out there, and asks questions regarding how or what can be proven given theobjects, some operations or relations amongst the objects, and a set of axioms.
		To give a flavor, mentioning the hyperreals and/or the extension of the concepts of basis and dimension to strongly minimal theories would begood.
	www.anoca.org /set/proof/model_theory.html (836 words)

	WMU News (Site not responding. Last check: 2007-10-21)
		When not on the air, Devlin serves as the dean of science and professor of mathematics at St. Mary's College in Moraga, Calif. He is also a senior researcher at Stanford University's Center for the Study of Language and Information.
		His ability to communicate mathematical ideas in a lucid and engaging manner and his efforts to promote public understanding of mathematics recently earned him the honor of being elected a lifetime Fellow of the American Association for the Advancement of Science.
		Devlin's visit to Western is sponsored by WMU's chapter of Pi Mu Epsilon mathematics honor society, the Science and Math Teacher Association, the Department of Mathematics and Statistics, and the Campus Activities Board.
	www.wmich.edu /wmu/news/2000/0010/0001-084.html (238 words)

	Arthur W. Apter
		Mathematical Logic, specifically Set Theory: Large Cardinals and Forcing.
		Slides from the lecture I presented at the Baumgartner 60th Birthday Conference, held October 4-5, 2003 at Dartmouth College can be found by clicking here for the.dvi file, and here for the LaTeX file.
		Sargsyan) "Can A Large Cardinal Be Forced From A Condition Implying Its Negation?", Proceedings of the American Mathematical Society 133, 2005, 3103-3108.
	faculty.baruch.cuny.edu /apter (1418 words)

	vita
		Teaching a 24 semester-hour per year load in a broad range of undergraduate mathematics courses, research in differential equations, dynamical systems and mathematical modeling, Linux system administration, development of distance and digital education courseware, WWW page development, development of components of the applied mathematics curriculum, and other service.
		``Forcing of Solutions to Reaction-Diffusion Equations With Applications to Population Models,'' a talk given 10/12/2002 at the 22nd Annual South Eastern Atlantic Regional Conference on Differential Equations, University of Tennessee, Knoxville, TN, USA (10/11/2002-10/12/2002).
		Chair of the Department of Mathematics Student Evaluation Committee; responsible for verifying that students have met all requirements for graduation at the time they apply to graduate, keeping lists of students receiving departmental honors, and counseling students on academic probation; 09/2004-present.
	banach.millersville.edu /~bob/vita (2540 words)

	Prof S J Hogan
		There is a huge untapped reservoir of significant engineering, industrial and other problems where mathematics can be applied in novel and useful ways or which require innovative non-standard mathematics.
		It is situated in the Department of Engineering Mathematics in the Faculty of Engineering.
		London Mathematical Society grant (with Dr. Budd) to put on a one-day meeting in Bristol on the Mathematics of Impact.
	www.enm.bris.ac.uk /anm/staff/sjh.html (955 words)

	Citebase - Norms on possibilities II: more ccc ideals on 2^{omega} (Site not responding. Last check: 2007-10-21)
		We present a systematic study of the method of "norms on possibilities" of building forcing notions with keeping their properties under full control.
		We present reasons for developing a theory of forcing notions which satisfy the properness demand for countable models which are not necessarily elementary submodels of some (H(chi), in).
		Iteration of lambda-complete forcing notions not collapsing lambda
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/9703222 (990 words)

	The Mathematics Genealogy Project - Curtis Herink
		Mathematics Subject Classification: 03 — Mathematical logic and foundations
		The Mathematics Genealogy Project is a service of the Department of Mathematics, North Dakota State University.
		The genealogy project is in need of funds to help pay for student help and such.
	genealogy.math.ndsu.nodak.edu /html/id.phtml?id=9606 (84 words)

	Category:Set theory - Wikipedia, the free encyclopedia
		Articles on this topic in other Wikimedia projects can be found at: Wikimedia Commons Category Set theory
		Set theory is any of a number of subtly different things in mathematics:
		Naive set theory is the original set theory developed by mathematicians at the end of the 19th century, treating sets simply as collections of things.
	en.wikipedia.org /wiki/Category:Set_theory (181 words)

	Dr Milan Grulovic (Site not responding. Last check: 2007-10-21)
		He has taught courses in Algebraic Structures, Universal Algebra, Mathematical Logic, Linear Algebra and Mathematics for students of Technology and Physics.
		His mathematical interests are in model theory, model-theoretic forcing and topological model theory.
		At present he is a reviewer for Mathematical Reviews and a member of the Associaation for Mathematical Logic.
	www.im.ns.ac.yu /faculty/grulovicm (202 words)

	Souslin Absoluteness, Uniformization and (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		Regularity properties of projective sets Eyal Amir Dept. of Mathematics and...
		1 Souslin forcing and additivity of measure (context) - Bagaria, Judah et al.
		1 Combinatorial properties of Hechler forcing (context) - Brendle, Judah et al.
	citeseer.ist.psu.edu /697968.html (426 words)

	Forcing Structures and Cliques in Uniquely Vertex Colorable Graphs
		Forcing Structures and Cliques in Uniquely Vertex Colorable Graphs: SIAM Journal on Discrete Mathematics Vol.
		In this paper, first we introduce a technique called forcing.
		Then by applying this technique in conjunction with a feedback structure we construct a k-UCG with clique number k-t, for each $t \geq 1$ and each k, when k is large enough.
	epubs.siam.org /sam-bin/dbq/article/30499 (248 words)

	Mathematics (Site not responding. Last check: 2007-10-21)
		Starter should release the cart without pushing in spring (force) and observe.
		Starter should push spring (force) in half way, by forcing against the wall, and release.
		Starter should push spring in all the way, by forcing against the wall all the way, and release.
	www.iit.edu /~smile/mp0198.htm (216 words)

	Faculty Members by Ares of Interest
		Numerical methods in mathematical physics, solution of integro-differential equations and their asymptotic development.
		Nineteenth and early twentieth century mathematics, relations between the history and the pedagogy/teaching of mathematics.
		Shenitzer, Ph.D. History and philosophy of mathematics and their uses in the teaching of mathematics.
	www.math.yorku.ca /Grad/99-00/interest.html (509 words)

	[No title]
		Part A}, volume = {46}, year = {1983}, }, @article{Sh:87b, author = {Shelah, Saharon}, ams-subject = {(03C45)}, fromwhere = {IL}, journal = {Israel Journal of Mathematics}, review = {MR 85m:03024b}, pages = {241--273}, title = {Classification theory for nonelementary classes, I. The number of uncountable models of $\psi \in L_{\omega _{1},\omega }$.
		Next, we present a model where there is a $\sigma$-linked not $\sigma$-centered Souslin forcing such that all its small subsets are $\sigma$-centered but Martin Axiom fails for this order.
		Furthermore, we construct a totally nonhomogeneous Souslin forcing and we build a Souslin forcing which is proper but not ccc that does not contain a perfect set of mutually incompatible conditions.
	shelah.logic.at /shelah_a.bib (1856 words)

	[No title]
		“A Novel Digital Communication System using Logistic Map”, Monthly Colloquium of Center of Computational Sciences and Scientific Visualization, School of Mathematics, Science and Technology, Elizabeth City State University, Elizabeth City, January 24, 2002.
		International Conference on Technology in Teaching Mathematics, University of Plymouth, August 1999, Plymouth, England.
		Estimation of number of conjugacy classes of finitely generated function groups”, American Mathematical Society meeting, November 1995,
	www.ecsu.edu /ECSU/AcadDept/MathandCS/dcsengupta/Presentations.htm (304 words)

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