Related papers: Model Theory of the Inaccessibility Scheme
We introduce the notion of first order amenability, as a property of a first order theory $T$: every complete type over $\emptyset$, in possibly infinitely many variables, extends to an automorphism-invariant global Keisler measure in the…
Nearly linear recurrences are a generalisation of linear recurrences and are instances of linear time-invariant systems in control theory and linear constraint loops in program analysis. In this paper we formulate the Positivity Problem for…
We present an overview of results on the question of whether the non-stationary ideal of an uncountable regular cardinal $\kappa$ can be defined by a $\Pi_1$-formula using parameters of hereditary cardinality at most $\kappa$. These results…
A countable structure is said to be extendible if it has the same Scott sentence as some uncountable structure. Rigid structures are not extendible. We give an example of an extendible model with a rigid elementary extension.
We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…
Originally introduced by Kolmann and Shelah as a surrogate for saturated models, limit models have been established as natural and useful objects when studying abstract elementary classes. Shelah began the study of when (multiple notions…
This dissertation includes many theorems which show how to change large cardinal properties with forcing. I consider in detail the degrees of inaccessible cardinals (an analogue of the classical degrees of Mahlo cardinals) and provide new…
In this paper, the reachability of dimension-bounded linear systems is investigated.Since state dimensions of dimension-bounded linear systems vary with time, the expression of state dimension at each time is provided.A method for judging…
A result of Kaufmann shows that if $L_\alpha$ is countable, admissible and satisfies $\Pi_n\textsf{-Collection}$, then $\langle L_\alpha, \in \rangle$ has a proper $\Sigma_{n+1}$-elementary end extension. This paper investigates to what…
We investigate the extent of second order characterizable structures by extending Shelah's Main Gap dichotomy to second order logic. For this end we consider a countable complete first order theory T. We show that all sufficiently large…
We prove under $V=L$ that the inclusion modulo the non-stationary ideal is a $\Sigma_1^1$-complete quasi-order in the generalized Borel-reducibility hierarchy ($\kappa>\omega$). This improvement to known results in $L$ has many new…
We study the model-checking problem for first- and monadic second-order logic on finite relational structures. The problem of verifying whether a formula of these logics is true on a given structure is considered intractable in general, but…
We give an almost entirely model-theoretic account of both Ramsey classes of finite structures and of generalized indiscernibles as studied in special cases in (for example) [7], [9]. We understand "theories of indiscernibles" to be special…
The additivity spectrum ADD(I) of an ideal I is the set of all regular cardinals kappa such that there is an increasing chain {A_alpha:alpha<kappa\} in the ideal I such that the union of the chain is not in I. We investigate which set A of…
The category of models of any theory $T$ in any first-order language $L$ has the surprising property that any small category that is elementarily equivalent with it, already embeds in it. The proof uses an abstract argument via ultrapowers,…
We answer a variant of a question of Rodl and Voigt by showing that, for a given infinite cardinal lambda, there is a graph G of cardinality kappa =(2^lambda)^+ such that for any colouring of the edges of G with lambda colours, there is an…
We investigate a model theoretic invariant $\kappa_{srd}^m(T)$, which was introduced by Shelah in his famous book, and prove that $\kappa_{srd}^m(T)$ is sub-additive. When $\kappa_{srd}^m(T)$ is infinite, this gives the equality…
We consider the problem of symbolic reachability analysis of higher-order context-free processes. These models are generalizations of the context-free processes (also called BPA processes) where each process manipulates a data structure…
According to the math tea argument, there must be real numbers that we cannot describe or define, because there are uncountably many real numbers, but only countably many definitions. And yet, the existence of pointwise-definable models of…
The work presents the brief exposition of the proof (in ZF) of inaccessible cardinals nonexistence. To this end in view there is used the apparatus of subinaccessible cardinals and its basic tools -- reduced formula spectra and matrices and…