# Tagged Questions

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### Gödel's incompleteness theorems: where to learn? Is there a straightforward relation between the two?

What would be a good textbook or paper to learn the proofs of the two Gödel's incompleteness theorems from? I would prefer it to be as close to the original proofs as possible. I have not tried to ...
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### Modern book on Gödel's incompleteness theorems in all technical details

Is there a modern book on Gödel's incompleteness theorems that goes into each and every technical aspect of the proof of them (a classical one, if such exists)? I'm not interested in popular ...
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### Putting down axioms for some symbols. Playing with their consequences qualitatively and symbolically. Building theories. The book?

I am interested in the design and building of theories. By building theories, I mean putting down axioms of various kinds, over various fields, exploring their perhaps interesting, or probably boring, ...
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### Intuitionistic Linear Logic

I am currently going through some papers that use the "intuitionistic version" of Girard's Linear Logic. Problem is, i seem to find very little literature on it. There is a lot done on Linear Logic ...
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### I would like some textbook recommendations for model theory

I am a 3rd year undergraduate math student and would like to study model theory. . I have some background with set theory, ordinals etc and also with mathematical logic. This is purely for self study ...
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### Suggestion for independent study of mathematical logic

Hello I'm looking for advice on mathematical logic books that are good for self-study. I would really like a text that has some if not all of the answers to exercises so I can check my progress as I ...
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### The Consistency of Arithmetic

I believe that within ZFC (or maybe even a weaker subset of ZFC) there is a proof of $\mathbb{N}=(\omega,+,.,<,0,1)\models{PA}$. What would be a standard reference for this?
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In my opinion, a cool definition of "algebraic signature" is as follows: An algebraic signature on the sort symbols $\mathcal{X} = \{X_0,...,X_{n-1}\}$ is precisely a quiver whose underlying set ...
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### Reference for problems without efficient algorithm (in polynomial time)

I'm writing paper and need your help in finding some famous (or not so famous) problems without efficient algorithm, but from logic or computer science. So far, I have: -Boolean satisfiability ...
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### Metatheoretical terms for logic

When we study logic we define various metatheoretic properties for logical systems and first-order theories, and then ask whether particular systems or theories have these properties. "Consistent" and ...
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### Book request: mathematical logic with a semantical emphasis.

Suppose I am interested in the semantical aspect of logic; especially the satisfaction $\models$ relation between models and sentences, and the induced semantic consequence relation $\implies,$ ...
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### Construction of a Kurtz random sequence that's not Martin-Löf random

How can one construct a Kurtz random sequence that's not Martin-Löf random? I'm also interested in the paper that included the first of such constructions. I suspect it was in Kurtz's dissertation, ...
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### Textbook on Basics of Formal Systems

Whilst trying to learn more about logic I came across Smullyan's Theory of Formal Systems on Google Books. What I liked about the book was how clearly it managed to describe (on pages 3-5 in chapter ...
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### Book for teaching mathematic and IQ for kid.

I'm finding some books talk about teaching mathematic for kid ,logic and IQ for kid. Can you present for me some books?
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### Good books for building number/math intuition

I'm wondering if there are some good book/textbooks that were designed with algebraic logic in mind (ie. building intuition rather than rote learning). As an example of what I mean, consider this ...
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### Conservativity theorem

There is an article in Wikipedia titled "Conservativity theorem" - see http://en.wikipedia.org/wiki/Conservativity_theorem I have looked through a dozen of mathematical logic textbooks, but could ...
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### Advice regarding best-practice mathematics / categorial logic.

A good heuristic is: If it doesn't cost anything, generalize. In particular, if we have a theorem, and a proof thereof, then we ought to look for a maximal generalization of this theorem, ...
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### How to prove “basic” identities in first order logic?

On the Wikipedia page for First-order logic, there is a list of Provable Identities. Although they seem very basic, I can't find anyone giving a formal proof of them. In particular, consider one ...
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### where to start reading theory of logics?

I am a student who is working Lie Theory. I want to start read theory of logics. I just need some reference and I have few questions regarding this, i) will studying theory of logics will improve my ...
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### Book that is more accessible than Shoenfield

My logic course is based on my Computer Science education and on some random Internet pages (mostly Wiki). I want to make my knowledge of logic more coherent and fill in missing gaps. Thus I started ...
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### Genericity and category

This paper by Ambos-Spies and Mayordomo on the theory of algorithmic randomness introduces the notion of genericity saying that it is based on Baire category while the usual notion of randomness is ...
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### Fragments of first-order logic and the functions that preserve them - reference request.

Is there a good resource for learning about different fragments of first-order logic? At this point, I'm mainly just interested in the basic facts, nothing too deep, but preferably presented in a ...
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I am looking for books to read, so as to dive into mathematical logical and related disciplines like set theory, model theory, and topos theory. I have a decent background in category theory and ...
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### How would I know if I'm good in logic?

I've always been interested in logic, but unfortunately my school contains no logicians. What are some good logic puzzles/books and how would I know if logic is right for me? Also, what can I do with ...
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### Boolean prime ideal theorem and the axiom of choice

The Boolean prime ideal theorem is strictly stronger than ZF, and strictly weaker than ZFC. I'm looking for nice examples (like the existence of non-measurable set) that request at least that theorem ...
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Is there a name for the following (heuristic, informal) system of conventions for dealing with partial functions and undefined expressions? I'd like to know whether it has any undesirable quirks that ...
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### Con ZF implies Con ZFC using set sized models

Can we use forcing to construct models of ZFC and ZFC + GCH starting from c.t.m s of ZF? The usual way to obtain the associated relative consistency results (Con ZF implies Con ZFC and Con ZF implies ...