We introduce the notion of pseudo-algebraicity to study atomic models of first order theories (equivalently models of a complete sentence of Lω1,ω). Theorem: Let T be any complete first-order theory in a countable language with an atomic model. If the pseudo-minimal types are not dense, then there are 2א1 pairwise non-isomorphic atomic models of T , each of size א1.

Solving equations is one of the main themes in mathematics. A large part of the combinatorial group theory revolves around the word and conjugacy problems particular types of equations in groups. Whether a given equation has a solution in a given group is, as a rule, a non-trivial problem. A more general and more difficult problem is to decide which formulas of the first-order logic hold in a g...

It is shown that the positive first-order theory of an HNN-extension G = 〈H, t; tat = φ(a)(a ∈ A)〉 can be reduced to the existential firstorder theory of G provided that A and B are proper subgroups of the base group H with A∩B finite. For an amalgamated free product G = H ∗A J , we show that the positive first-order theory of G can be reduced to the existential first-order theory of G in case ...

The aim of this paper is to give a new proof for the decidability and nite model property of rst-order logic with two variables (without function symbols), using a combinatorial theorem due to Herwig. The results are proved in the framework of polyadic equality set algebras of dimension two (Pse 2). The new proof also shows the known results that the universal theory of Pse 2 is decidable and t...

This paper presents a theory of informative communications among agents that allows a speaker to communicate to a hearer truths about the state of the world; the occurrence of events, including other communicative acts; and the knowledge states of any agent — speaker, hearer, or third parties — any of these in the past, present, or future — and any logical combination of these, including formul...

In this paper we present some of our school’s results in the area of building up relativity theory (RT) as a hierarchy of theories in the sense of logic. We use plain first-order logic (FOL) as in the foundation of mathematics (FOM) and we build on experience gained in FOM. The main aims of our school are the following: We want to base the theory on simple, unambiguous axioms with clear meaning...