# Tagged Questions

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### Most suitable book after Bergmann Logic Book

I'd like to know what the best book would be to pick up after this one would be. Essentially, it covers basic logical concepts (validity, soundness, consistency) and goes on to sentential and ...
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### Universal quantifiers that are interpreted “almost-everywhere”

Often sentences that are false, are nonetheless "true almost everywhere." Example 0. The integers do not satisfy the cancellation law: $$\forall a\forall xy(ax = ay \rightarrow x=y)$$ This is ...
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### A Question Regarding Consistent Fragments of Naive (Ideal) Set Theory

It is well known that Naive (to some, otherwise known as Ideal) set theory, that is, the set theory generated by the axioms: (EXT) (x)(x $\in$ A iff x $\in$ B) iff A=B (COMP) ($\exists$y)(x)(x ...
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### Representation theorem for Heyting algebras?

A fundamental theorem by Stone asserts that any Boolean algebra is isomorphic to a subalgebra of the archetypical Boolean algebras, that is the power sets of a set $X$ (equipped with intersection, ...
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### Introductions to classical and nonclassical logic?

I've found Eric Schechter: Classical and Nonclassical Logics: An Introduction to the Mathematics of Propositions a really nice book. But I'd like to skim through other books about the same subject, at ...
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### Partial order on cardinalities without the axiom of choice

Cardinality can still be defined without choice, e.g. as equivalence class of equipotent sets, see Defining cardinality in the absence of choice. Injections define partial order on cardinalities by ...
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### Book about different kind of logic

I'm searching for a book that talks about different kind of logic ( esoteric and particular one too ) and their uses and differences. Does such a book exist?
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### Is this a good way to (or correct) proof?

Given: P ⇒ Q. To show: ¬Q ⇒ ¬P. Using modus tollens: Assume that ¬Q. Then ¬P. Thus ¬Q ⇒ ¬P. Does anybody have a good reference to how I can learn how to proof such formulas (including ...
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### Best introduction to recursive functions

Hello I'm looking for a solid introduction to recursive functions within the domain of mathematical logic. I'm studying logic and would like to become more informed about this area of theory. I would ...
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### Modal set-theory

In his “The Potential Hierarchy of Sets”, Review of Symbolic Logic 6:2 (2013), 205-28 Øystein Linnebo has proposed a modal set-theory. I was wondering what kind of utility can such a theory have for a ...
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### Graduate level elementary logic books

I've done two courses on Logic during my Bachelor course, but they were very basic. Now I'm going to start by PhD, and I'm interested in learning "real Logic". Could you please provide some references ...
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### Logic in closed symmetric monoidal categories; reference request.

Suppose we want an algebraic theory $T$ to be interpretable in any closed symmetric monoidal category $\mathbf{C}.$ I am thinking in particular of the case where $\mathbf{C}$ is the category of models ...
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### Help with positive- and negative-forms in Proof Theory

I need help in understanding a device used bu Kurt Schütte, Proof Theory (1977). In treating classical sentential calculus, he use - in place of truth-tables - the device of positive- and ...
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### Some reference for categorical logic?

By "categorical logic" I mean category-theoretical models of logic. In particular, I am more interested in models of intuitionistic predicate logic with conjunction, disjunction, implication and ...
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### Online lectures for a first course in mathematical logic

I have a friend who is interested in learning math. I suggested that he learns mathematical logic. He has never learnt mathematical logic before, however I believe he has all the necessary ...
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### The deep structure of logical formulas

A long-standing question to which I never found a concise answer is: Is there something like an unambiguous deep structure of a formula of propositional logic, opposed to its comparingly ...
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### Founding Arithmetic on geometry

In the past I found some fleeting references that some (Frege in his later years being one of them) tried to found arithmetic not on set-theory and logic but on geometry and logic. Unfortunedly Frege ...
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### Can one define $\langle x,y\rangle$ in $P(C)$?

I study at course Foundations of Mathematics the below definitions and lemma: $\langle x,y\rangle:=\{\{x\},\{x,y\}\}$ (from Kuratowski 1921) $\langle x,y\rangle:=\{\{\{x\},\varnothing\}\{\{y\}\}\}$ ...
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### Certain sequents as inference rules

Fix a signature $\sigma.$ Then a coherent formula is a first-order formula built using only $\{\wedge,\vee,\top,\bot,\exists\}.$ See the link for more information. Furthermore, by a "special" ...
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### Recommendation on a rigorous and deep introductory logic textbook

In this post, I don't mean any word by its somewhat "mathematical or logical" meaning but just "literally". It's been three years since I started "formal" mathematics, and now I'm familiar with set ...
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### T-norms with arity 3

I'm working on some 3D vectors with fuzzy values, and I'd like to devise some operations on them. After my brief search, I haven't been able to find any existing work on t-norms with arity n>2. Is ...
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### Elementary references on Robinson Arithmetic, Prim. Recursive fns etc.

I'm in the middle of revising my freely available and much-downloaded introductory notes Gödel Without (Too Many) Tears. (They are a sort of cut down version of part of my Gödel book, and I'm ...
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### Mathematical logic book with answers to exercises

I'm sure a question similar to mine has been asked before, but I am looking for a mathematical logic book with answers to the exercises. I am studying independently and although I have good logic ...
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### Good textbook for learning Sequent Calculus

There are many modern text books teaching logic using Natural Deduction. There are no books teaching logic using the axiomatic method (see Good book for learning and practising axiomatic logic ) Now ...
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### Books/papers on model theory in non-monotonic logic

I am working on a project whose object language is in non-monotonic logic. Since the project involves reasoning about the models, I am thinking of translating a non-monotonic problem into a ...
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### Logic and set theory textbook for high school

Do you have any advice for a textbook or a book for high schools students which completely adresses basics of logic (proposition, implication, and, or, quantifiers) and set theory (intersection, ...
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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?