Provability, Computability and Reflection.

This paper presents a monotonic system of Post algebras of order +* whose chain of Post constans is isomorphic with 012 ... -3-2-1. Besides monotonic operations, other unary operations are considered; namely, disjoint operations, the quasi-complement, succesor, and predecessor operations. The successor and predecessor operations are basic for number theory.

Terence Irwin's edition of the Nicomachean Ethics offers more aids to the reader than are found in any modern English translation. It includes an Introduction, headings to help the reader follow the argument, explanatory notes on difficult or important passages, and a full glossary explaining Aristotle's technical terms. The Third Edition offers additional revisions of the translation as well as revised and expanded versions of the notes, glossary, and Introduction. Also new is an appendix featuring translated selections from related texts (...) of Aristotle. (shrink)

Post algebras of order + as a semantic foundation for +-valued predicate calculi were examined in [5]. In this paper Post spaces of order + being a modification of Post spaces of order n2 (cf. Traczyk [8], Dwinger [1], Rasiowa [6]) are introduced and Post fields of order + are defined. A representation theorem for Post algebras of order + as Post fields of sets is proved. Moreover necessary and sufficient conditions for the existence of representations preserving a given (...) set of infinite joins and infinite meets are established and applied to Lindenbaum-Tarski algebras of elementary theories based on +-valued predicate calculi in order to obtain a topological characterization of open theories. (shrink)