A mathematical introduction to logic
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在 Hacker News 阅读原文…standing of what they mean. They all have clear technical meanings. If you're interested in this stuff and can stomach mathematical rigor, I highly recommend Enderton's _A Mathematical Introduction to Logic_ for mathematical logic in general, and Smullyan's own _Goedel's Incompleteness Theorems_ for this topic. Now, to back my harsh words a little. An axiomatic system, in the context of Goedel's theorems, is a bunch of axioms with some inference rules. Axioms are statements that are automatically taken as proved, while inference rules allow one to infer more proved statements from some already proved statements. Given an axiomatic system, you can define a proof of statement X to be a sequence of statements that starts with axioms and always goes through inference rules until it reaches X. All of the above is purely syntactic, meaning it h…
在 Hacker News 阅读原文I rate Enderton's A Mathematical Introduction to Logic . http://www.math.ucla.edu/~hbe/amil/index.html
在 Hacker News 阅读原文… of set theory and mathematical logic. Each were the basis for the course I took on the topic, and recieved pretty good reviews on Amazon: Karel Hrbacek and Thomas Jech, Introduction to Set Theory. ISBN-13: 978-0824779153. Herbert Enderton, A Mathematical Introduction to Logic. ISBN-13: 978-0122384523. Hope this helps. :-)
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