Search results

logic, two structures M and N of the same signature σ are called elementarily equivalent if they satisfy the same first-order σ-sentences. If N is a substructure...

based on game semantics for determining whether two structures are elementarily equivalent. The main application of Ehrenfeucht–Fraïssé games is in proving...

P} is prime if it admits an elementary embedding into any model M {\displaystyle M} to which it is elementarily equivalent (that is, into any model M {\displaystyle...

Benacerraf's identification problem. Benacerraf noted that there are elementarily equivalent, set-theoretic ways of relating natural numbers to pure sets. However...

meta-level, set-theoretic falsehood, namely in relation to other elementarily-equivalent set-theories not identical to the one chosen. The identification...

theorem, the degree of this extension is necessarily 2, and F is elementarily equivalent to R. Such fields are also known as real closed fields. Any field...

fields have equivalent valuation groups and residue fields, and the residue fields have characteristic 0, then they are elementarily equivalent (which means...

need not be a strongly minimal theory, that is, there may be an elementarily equivalent structure that is not minimal. O-minimal structures can be defined...

over its minimal convex subgroup is divisible. Such groups are elementarily equivalent to the integers ( Z , + , < ) {\displaystyle (\mathbb {Z} ,+,<)}...

word-hyperbolic groups and to characterize all groups that are elementarily equivalent to (that is, have the same first-order theory as) a given torsion-free...

consistent, effective first-order theory has models that are not elementarily equivalent, a stronger limitation than the one established by the Löwenheim–Skolem...

ultrapowers, they are elementarily equivalent. The Keisler-Shelah theorem provides a converse: If M and N are elementary equivalent, then there is a set...

field is a field F in which any of the following equivalent conditions is true: F is elementarily equivalent to the real numbers. In other words, it has the...

show that any two countable atomic models of a theory that are elementarily equivalent are isomorphic. Some authors refer to complete formulas as "atomic...

row equivalent if one can be changed to the other by a sequence of elementary row operations. Alternatively, two m × n matrices are row equivalent if and...

satisfies the substitution axioms for equality can be cut down to an elementarily equivalent interpretation on a subset of the original domain. Thus there is...

constant, defined as the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron...

whether two model-theoretic structures were elementarily equivalent. This method of determining elementary equivalence was later formulated as the Ehrenfeucht–Fraïssé...

any structure containing it. Two structures are defined to be elementarily equivalent if they agree about the truth value of all sentences in their shared...

p-adically closed fields as those whose first-order theory is elementarily equivalent to that of Q p {\displaystyle \mathbb {Q} _{p}} . Ax & Kochen (1965)...