What people are saying - Write a review
We haven't found any reviews in the usual places.
Szmielews Product Construction
Sentences Determining Elementary
Eliminating Quantification from
2 other sections not shown
arbitrary Abelian group Assume basic classes basic sentences cardinal number CHAPTER class of Abelian classes are elementary closed formula construct couples p,k cyclic group decidable theory DECISION PROBLEM decompose F direct products Ehrenfeucht criterion elementarily equivalent elementary classes elementary theory elements x0 eliminating quantification Ershov Feferman-Vaught finite number finite sets following theorem free variables function F game Gn game of length Godel number H 3(k+J Hence implies independent mod pk isomorphism kind iff linearly independent mod linearly independent modulo M-j_ M2 are indiscernible maximal set natural numbers number of elements nx=C obtain order pk pk and strongly pk+1 player II wins positive integer Proof q 0 otherwise recursive axiom system recursively axiomatizable theory sequence of elements set Nom(T set of elements specified by sentence strongly linearly independent stsf stsfM2 Szmielew theory of Abelian torsion-free TT TT winning strategy xk+-j_