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A simpler axiomatization of the Shelah-Spencer almost sure theories
Shelah-Spencer almost sure theories
2015/9/28
We give an explicit AE-axiomatization of the almost sure theories
of sparse random graphs G(n, n−α) of Shelah-Spencer. In the process
we give a method of constructing extensions of graphs whos...
Mutually algebraic structures and `automatic' quantifier elimination
Mutually algebraic structures `automatic' quantifier elimination
2015/9/28
Mutually algebraic structures and `automatic' quantifier elimination.
Characterizing model completeness among mutually algebraic structures
algebraic structures model completeness
2015/9/28
We characterize when the elementary diagram of a mutually algebraic
structure has a model complete theory, and give an explicit
description of a set of existential formulas to which every formula
i...
Mutually algebraic structures and expansions by predicates
algebraic structures predicates
2015/9/28
We introduce the notions of a mutually algebraic structures and
theories and prove many equivalents. A theory T is mutually algebraic
if and only if it is weakly minimal and trivial if and only if n...
The elementary diagram of a trivial, weakly minimal structure is near model complete
elementary diagram model complete
2015/9/28
We prove that if M is any model of a trivial, weakly minimal theory,
then the elementary diagram T(M) eliminates quantifiers down
to Boolean combinations of certain existential formulas.
On the computability-theoretic complexity of trivial, strongly minimal models
computability-theoretic strongly minimal models
2015/9/28
We show the existence of a trivial, strongly minimal (and thus
uncountably categorical) theory for which the prime model is computable and
each of the other countable models computes 0
00. This res...
Model completeness for trivial, uncountably categorical theories of Morley rank one
uncountably categorical theories Model completeness
2015/9/28
The present paper is a direct continuation of [2], where it is shown that any strongly
minimal trivial theory is model complete after naming constants for a model. In this
paper we show that this re...
Trivial, strongly minimal theories are model complete after naming constants
model complete naming constants
2015/9/25
We prove that if M is any model of a trivial, strongly
minimal theory, then the elementary diagram Th(MM ) is a model
complete LM -theory. We conclude that all countable models of
a trivial, strong...
Borel complexity of complete, first order theories(status report)
first order theories status report
2015/9/25
Borel complexity of complete, first order theories(status report).
The rise and fall of uncountable models.
A Vaught’s conjecture toolbox.
We give a model theoretic proof that if there is a counterexample to Vaught’s conjecture there is a
counterexample such that every model of cardinality ℵ1 is maximal (strengthening a result of ...
Borel completeness of some aleph_0 stable theories
Borel completeness some aleph_0 stable theories
2015/9/25
We study ℵ0-stable theories, and prove that if T either has eniDOP
or is eni-deep, then its class of countable models is Borel complete.
We introduce the notion of λ-Borel completeness and pro...
P-NDOP and P-decompositions of aleph_epsilon saturated models of superstable theories
P-NDOP P-decompositions
2015/9/25
Given a complete, superstable theory, we distinguish a class P of
regular types, typically closed under automorphisms of C and non-
orthogonality. We define the notion of P-NDOP, which is a weakenin...
ω-stable theories: Do uncountable languages matter?
ω-stable theories uncountable languages matter
2015/9/25
ω-stable theories: Do uncountable languages matter?