In 1922, Fraenkel and Thoralf Skolem independently proposed operationalizing a " definite " property as one that could be formulated as a first order theory whose atomic formulas were limited to set membership and identity.
12.
Classification theory involves deep work over hundreds of papers to completely solve the spectrum problem on classification of first order theories in terms of structure and number of nonisomorphic models, a huge tour de force.
13.
Kleene remarks that " the predicate calculus ( without or with equality ) fully accomplishes ( for first order theories ) what has been conceived to be the role of logic " ( Kleene 1967 : 322 ).
14.
Prior to joining UC San Diego in 1994, she taught at Tufts University from 1974 until 1978, where she worked on computational complexity problems such as the theory of rational order and first order theory of real addition.
15.
A first order theory \ mathcal { QS } is a first-order theory with identity if \ mathcal { QS } includes the identity relation symbol " = " and the reflexivity and substitution axiom schemes for this symbol.
16.
He argues that if the meaning of a first-order scientific theory depends on its second-order theory of meaning, then two first order theories will be meta-incommensurable if they depend on substantially different theories of meaning.
17.
Sela pushed this work further to study first-order theory of arbitrary torsion-free 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 word-hyperbolic group.
