Caros colegas:
Trata-se do livro The Foundations of Mathematics, de Kenneth Kunen, publicado em 2009. Está disponível no sítio Gigapedia, no formato djvu. Segue o prefácio do mesmo: This book grew out of some notes for a beginning one semester graduate level course in logic at the University of Wisconsin in Madison. The author is grateful to the large number of students who contributed to the development of these notes, either by explicitly listing errors or by indicating informally that some parts of the text were unclear. The course, and this book, provide an introduction to set theory, model theory, and recursion theory. The expositions of set theory and model theory start from scratch and, in the main, follow the line of presentation found in the standard specialized texts in these areas. Set theory is done first, so that the model theory chapter can make use of results on cardinal arithmetic and Zorn's lemma when proving the Lowenheim-Skolem Theorem and the Compactness Theorem. The model theory chapter also contains some material on models of set theory. This includes a discussion of the absoluteness of 1 properties, and an analysis of models such as HF = H(Aleph 0) (which satisfies all the ZFC axioms except Infinity) and H(Aleph 1) (which satisfies all the axioms except Power Set). This book does not do independence proofs (such as the independence of the Continuum Hypothesis from ZFC), but it does provide all the prerequisite model theory and set theory for understanding such proofs. The exposition of recursion theory may seem a bit unusual. The basic definition of "computable" and "decidable" is "1 on HF". This approach is well-known to logicians, but is uncommon in elementary texts. There are two reasons for taking this approach here. First, it is actually the one most useful in set theory, since now it's obvious that computable notions are absolute. Second, I found that many students in my course already had taken a course in recursion theory, either as undergraduates or in our own graduate logic program. Starting from scratch with a detailed discussion of abstract machines would have been extremely boring to half the class, but simply assuming this approach to be already known would have lost the other half. So, the "1 on HF" was a way of giving a rigorous definition of "computable" which was new to almost all the students in the class. a) Arthur Buchsbaum De: [email protected] [mailto:[email protected]] Em nome de Decio Krause Enviada em: quarta-feira, 4 de agosto de 2010 10:32 Para: Francisco Antonio Doria Cc: [email protected] Assunto: Re: [Logica-l] Resenha de Gödel sobre Skolem-- um deslize acerca dos modelos não standard Doria, Marcelo Refiro-me ao livro do Kunen "The Foundations of Mathematics", baixável pela gigapedia (Arthur certamente tem). Tá num exercício, mas tenho que achar pois não me lembro direito (não mexo com essas coisas com muito detalhe). Talvez alguém na lista saiba mais e melhor... D.
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