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Set existence axioms for general (not necessarily countable) stability theory

1987
*
Annals of Pure and Applied Logic
*

*Set*

*existence*

*axioms*

*for*

*stability*

*theory*233 bounded and we define 2;, II;, A;

*for*i = 0, 1 and j E o as is customarily done in ... The aim of this paper is to extend our work [5] by formulating

*set*

*existence*

*axioms*in a

*general*context that can accommodate model

*theory*of arbitrary (

*not*

*necessarily*

*countable*) languages and then ... H owever, the distinction between the

*countable*and the

*general*(i.e.,

*not*

*necessarily*

*countable*)

*theory*is

*not*very fashionable nowadays, neither in algebra nor in parts of model

*theory*because, except ...

##
###
Book Review: Stability in model theory

1989
*
Bulletin of the American Mathematical Society
*

Nowadays, we prefer the shorter name of "w-

doi:10.1090/s0273-0979-1989-15781-9
fatcat:os4nxovvu5f37km2xkzvsplqru
*stability*." co-stable*theories*are*not**necessarily*categorical in some uncountable power but have good algebraic properties. ... Notice that L and, hence, T are allowed to have*not*only*countable*but also uncountable cardinalities, a fact that increases the scope of model*theory*. ...##
###
Book Review: Fundamentals of stability theory

1989
*
Bulletin of the American Mathematical Society
*

One may also look at more concrete contexts, arising

doi:10.1090/s0273-0979-1989-15757-1
fatcat:4hucuixuffainnri2kus6bwpni
*for*example in algebra, which are*not**necessarily*special cases of the abstract context. ... Shelah has completed the full first order case*for**countable**theories*[12] , and this will be in the second edition of [11] . ...##
###
The Stability Theory of Belief

2014
*
Philosophical Review
*

The

doi:10.1215/00318108-2400575
fatcat:rd4sy6mjwncnlhxi2pe77kt6j4
*theory*is based on three assumptions: the logical closure of rational belief; the*axioms*of probability*for*rational degrees of belief; and the so-called Lockean thesis, in which the concepts of rational ... of rational belief can be built around these principles that is*not*ad hoc but that has various philosophical features that are plausible independently. ... This is*not*just a random coincidence. From the principles of*stability**theory*, one can derive such correspondence results*for*conditionalization and belief revision in*general*; see Leitgeb 2013a. ...##
###
Remarks on generic stability in independent theories
[article]

2019
*
arXiv
*
pre-print

In NIP

arXiv:1905.11915v3
fatcat:ygeii5lisrcotkl4siqcs6wyl4
*theories*,*generically*stable Keisler measures can be characterized in several ways. We analyze these various forms of "*generic**stability*" in arbitrary*theories*. ... Among other things, we show that the standard definition of*generic**stability**for*types coincides with the notion of a frequency interpretation measure. ... In NIP*theories*, although*not*every type is*necessarily*definable and finitely satisfiable, the class of types with these properties is still quite resilient, and such types are now referred to as*generically*...##
###
Strategic stability in Poisson games

2014
*
Journal of Economic Theory
*

Furthermore, we use such a space to define the corresponding strategically stable

doi:10.1016/j.jet.2014.05.005
fatcat:rdtlgoqcfrbk7aee2cse5b25o4
*sets*of equilibria. ... We show that they satisfy*existence*, admissibility, and robustness against iterated deletion of dominated strategies and inferior replies. ... Every Poisson game has a stable set.Existence of stable*sets*in Poisson games is a particular case of a more*general**existence*result. ...##
###
STABILITY OF THE THEORY OF EXISTENTIALLY CLOSED S-ACTS OVER A RIGHT COHERENT MONOID S

2008
*
Advances in Algebra and Combinatorics
*

A

doi:10.1142/9789812790019_0009
fatcat:wfs7os2rqjamzhsrra75qjhqr4
*general*result of model*theory*says that S has a model companion, denoted by T S , precisely when the class E of existentially closed S-*sets*is axiomatisable and in this case, T S axiomatises E. ... It is known that T S*exists*and is stable if and only if S is right coherent. In the study of stable first order*theories*, superstable and totally transcendental*theories*are of particular interest. ... It is*not*difficult to see that if p ∈ S(∅) (so that*necessarily*I p = ∅), then*for*any G-*set*A there is exactly one extension p A of p in S(A) with I p A = ∅. ...##
###
Stability, the f.c.p., and superstability; model theoretic properties of formulas in first order theory

1971
*
Annals of Mathematical Logic
*

., some syntactical properties of uns able formulas, indiscernible

doi:10.1016/0003-4843(71)90015-5
fatcat:q62p6hgaw5gzppxwzhp333mcye
*sets*and degrees of types in superstable*theories*. ... Introduction List of results, conjectures and pv blems connected to*stability*§ 1. Notations § 2. Properties equivalent to unstabilit of formulas § 3. ... (See Def. 5.2.7 [See Shelah [D] Th. 3.1; IF] Th. 2.2, and here 5.8 are*generalizations*. ] There are some definitions of prime model; and proofs it*exists*under certain*stability*conditions. ...##
###
Stabilization of port-Hamiltonian systems with discontinuous energy densities

2022
*
Evolution Equations and Control Theory
*

<p style='text-indent:20px;'>We establish an exponential

doi:10.3934/eect.2021063
fatcat:2hqle3pzpbeupavldxcbjfrd2q
*stabilization*result*for*linear port-Hamiltonian systems of first order with quite*general*,*not**necessarily*continuous, energy densities. ... In particular, and in contrast to the previously known*stabilization*results, our result applies to vibrating strings or beams with jumps in their mass density and their modulus of elasticity.</p> ... I would like to thank the German Research Foundation (DFG)*for*financial support through the grant "Input-to-state*stability*and*stabilization*of distributed-parameter systems" (DA 767/7-1). ...##
###
Strong stochastic stability for non-uniformly expanding maps

2012
*
Ergodic Theory and Dynamical Systems
*

A weaker form of stochastic

doi:10.1017/s0143385712000077
fatcat:y57njtwnwncpfmafzoureyzklm
*stability*was established in [AAr03]*for*a*general*class of non-uniformly expanding maps, in the sense of convergence of the physical measure to the SRB probability measure ... Consequently, we are able to obtain the strong stochastic*stability**for*two examples of non-uniformly expanding maps. ... This does*not**necessarily*imply that f is non-uniformly expanding. ...##
###
Numerical stability of Euclidean algorithm over ultrametric fields

2017
*
Journal de Théorie des Nombres de Bordeaux
*

The memory of a computer being

doi:10.5802/jtnb.989
fatcat:ontuzlmyibgdngtmfzmegsdr2i
*necessarily*finite, it is*not*possible to represent exhaustively all elements of W . ... We also refer to [6]*for*a complete exposition of the*theory*including many discussions and examples. ... Numerical*stability*of Euclidean algorithm over ultrametric fields To conclude with, let us comment on briefly the hypothesis (H). ...##
###
The axiom of choice and model-theoretic structures
[article]

2019
*
arXiv
*
pre-print

We discuss the connections between the failure of the

arXiv:1908.11731v1
fatcat:bzfjzxdx7rh7tci7z4mqeqfa6i
*axiom*of choice in*set**theory*, and certain model-theoretic structures with enough symmetry. ... , but*not**necessarily*conversely. ... The disadvantage is that they work in a weaker*set**theory*, which we call FM, or possibly FMC (Fraenkel-Mostowski with choice) in which the*axiom*of extensionality is relaxed to allow the*existence*of ' ...##
###
On Zilber's field
[article]

2014
*
arXiv
*
pre-print

In this paper we use tools from

arXiv:1310.3777v6
fatcat:vzhl4jhnsnbwpes6sfefngkqva
*set**theory*and the uncountable categoricity of Zilber's pseudo-exponential field to show that Zilber's field is isomorphic to the complex field with (standard) exponentiation ... and hence Schanuel's conjecture holds*for*that field. ...*For*later use, we will assume more*generally*that M is a*countable*transitive well founded model of ZFC. (So the conclusions of this section will hold*for*any such model). ...##
###
Borovik-Poizat rank and stability
[article]

2007
*
arXiv
*
pre-print

Poizat raised the issue of the relationship between this notion of rank and

arXiv:0711.4040v1
fatcat:b5qku7m7gjampkw6remtof76vy
*stability**theory*in the following terms: "un groupe de Borovik est une structure stable, alors qu'un univers rangé n'a aucune ... These*axioms*form the basis of the algebraic treatment of groups of finite Morley rank which is common today. ... So if the*theory*of M is unstable, we may suppose that there is a definable relation R on a definable subset X of M eq such that R linearly orders some infinite subset of X,*not**necessarily*definable. ...##
###
Page 3381 of Mathematical Reviews Vol. , Issue 88g
[page]

1988
*
Mathematical Reviews
*

Andreas Blass (1-MI)
88g:03086 03F35 03C45
Harnik, Victor (IL-HAIF)

*Set**existence**axioms**for**general*(*not**necessarily**countable*)*stability**theory*.*Stability*in model*theory*(Trento, 1984). Ann. ... In this paper the author develops an extension of Friedman’s ax- iom systems of “reverse mathematics” to study which*set*-theoretic*existence**axioms*are necessary*for*model*theory*and algebra. ...
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