Related papers: A note on restriction rules
Infinite types and formulas are known to have really curious and unsound behaviors. For instance, they allow to type {\Omega}, the auto- autoapplication and they thus do not ensure any form of normalization/productivity. Moreover, in most…
The infinitary lambda calculi pioneered by Kennaway et al. extend the basic lambda calculus by metric completion to infinite terms and reductions. Depending on the chosen metric, the resulting infinitary calculi exhibit different notions of…
It has been shown in the late 1960s that each formula of first-order logic without constants and function symbols obeys a zero-one law: As the number of elements of finite models increases, every formula holds either in almost all or in…
Given a regular cardinal $\kappa$ such that $\kappa^{<\kappa}=\kappa$ (e.g., if the Generalized Continuum Hypothesis holds), we develop a proof system for classical infinitary logic that includes heterogeneous quantification (i.e., infinite…
$\Omega$-rule was introduced by W. Buchholz to give an ordinal-free cut-elimination proof for a subsystem of analysis with $\Pi^{1}_{1}$-comprehension. His proof provides cut-free derivations by familiar rules only for arithmetical…
We show that the Hrushovski-\fraisse limit of certain classes of trees lead to strictly superstable theories of various U-ranks. In fact, for each $ \alpha\in\omega+1\backslash\{0\} $ we introduce a strictly superstable theory of U-rank $…
We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…
We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…
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 axiomatic system introduced by H\'ajek axiomatizes first-order logic based on BL-chains. In this study, we extend this system with the axiom $(\forall x \phi)^2 \leftrightarrow \forall x \phi^2$ and the infinitary rule \[ \frac{\phi…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
For any first order theory T we construct a Boolean valued model M, in which precisely the T--provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a first order…
We extend the convergence law for sparse random graphs proven by Lynch to arbitrary relational languages. We consider a finite relational vocabulary $\sigma$ and a first order theory $T$ for $\sigma$ composed of symmetry and…
We consider first-order logic over the subword ordering on finite words, where each word is available as a constant. Our first result is that the $\Sigma_1$ theory is undecidable (already over two letters). We investigate the decidability…
This work is motivated by the problem of finding the limit of the applicability of the first incompleteness theorem ($\sf G1$). A natural question is: can we find a minimal theory for which $\sf G1$ holds? We examine the Turing degree…
The theory of limits of discrete combinatorial objects has been thriving for the last decade or so. The syntactic, algebraic approach to the subject is popularly known as "flag algebras", while the semantic, geometric one is often…
A complete partition theory is presented for omega-located words (and omega-words), namely for located words over an infinite alphabet dominated by a fixed increasing sequence. This theory strengthens in an essential way the classical…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
Let \phi be a first order formula and M be a countable model. \phi^M denotes the set of all assignments that satisfy \phi in M. Let M, N be countable models. A formula \phi distinguishes these models if |\phi^M|\neq |\phi^N|. We show that…
We to a large extent sort out when does a (first order complete theory) T have a superlimit model in a cardinal lambda . Also we deal with relation notions of being limit.