Sequential theories and infinite distributivity in the lattice of chapters

Journal of Symbolic Logic 54 (1):190-206 (1989)
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Abstract

We introduce a notion of complexity for interpretations, which is used to prove some new results about interpretations of sequential theories. In particular, we give a new, elementary proof of Pudlák's theorem that sequential theories are connected. We also demonstrate a counterexample to the infinitary distributive law $a \vee \bigwedge_{i \in I} b_i = \bigwedge_{i \in I} (a \vee b_i)$ in the lattice of chapters, in which the chapters a and b i are compact. (Counterexamples in which a is not compact have been found previously.)

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Citations of this work

Cardinal arithmetic in the style of Baron Von münchhausen.Albert Visser - 2009 - Review of Symbolic Logic 2 (3):570-589.
Interpretability degrees of finitely axiomatized sequential theories.Albert Visser - 2014 - Archive for Mathematical Logic 53 (1-2):23-42.

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Review: Alfred Tarski, Undecidable Theories. [REVIEW]Martin Davis - 1959 - Journal of Symbolic Logic 24 (2):167-169.

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