Intereting Posts

How to Classify $2$-Plane Bundles over $S^2$?
When is the difference of two convex functions convex?
A prime ideal with the algebraic set reducible
Expected number of coin tosses to land n heads
Lower hemicontinuity of the intersection of lower hemicontinuous correspondences
A non-UFD such that $a^2 \mid b^2$ does not lead to $a\mid b$
Prove or disprove statements about the greatest common divisor
A Polygon is inscribed in a circle $\Gamma$
How to solve a bivariate quadratic (not necessarily Pell-type) equation?
Permutation & Combination
Characteristic time?
In how many ways can we put $31$ people in $3$ rooms?
Is there a good “bridge” between high school math and the more advanced topics?
How many roots have modulus less than $1$?
Exists $C = C(\epsilon, p)$ where $\|u\|_{L^\infty(0, 1)} \le \epsilon\|u'\|_{L^p(0, 1)} + C\|u\|_{L^1(0, 1)}$ for all $u \in W^{1, p}(0, 1)$?

I’m a civil engineer that spends all of its free time (with the permission of my wife and my two children) studying set theory and mathematical logic. For instance, I’ve read and enjoyed “Axiomatic set Theory” by Suppes, Enderton’s “Elements of set theory”,”Mathematical logic” by Shoenfield or “A course in mathematical logic” by Bell and Machover. Now, my goals are the history and the development of these two mathematical branches.

In this sense I’m reading “Foundations of Set Theory” by Fraenkel, Bar-hilleil and levy or “Labyrinth of thought” by José Ferreirós and I would like to have in the same line as the above good books in the foundations of mathematical logic.

Thank you in advance

- Are variables logical or non-logical symbols in a logic system?
- Difference between elementary submodel and elementary substructure
- Ideas about Proofs
- Prove that a set of connectives is inadequate
- Associativity of $\iff$
- axioms of equality

- $2\mathbb Z$ is not a definable set in the structure $(\mathbb Z, 0, S,<)$
- Concrete example for diagonal lemma
- Order of cyclic groups and the Euler phi function
- Negation of if and only if?
- Good abstract algebra books for self study
- What are power series used for? (a reference request)
- If the union of two sets is contained in the intersection, then one is contained in the other ($\implies A \subseteq B$)
- Reference for matrix calculus
- Embeddings are precisely proper injective immersions.
- What can we say about the kernel of $\phi: F_n \rightarrow S_k$

The reading list/study guide linked at http://www.logicmatters.net/students/tyl/ is only half done yet [reminder to self to get on with it!] but might contain one or two helpful suggestions.

You might like the book “Foundations of Mathematics” by William S. Hatcher.

You might be interested in van Heijenoort’s From Frege To Gödel: A Source Book in Mathematical Logic, 1879-1931.

On a different line, I recommend Dauben’s biography of Cantor, and his more recent Battle for Cantorian Set Theory.

*Introduction to Mathematical Thinking* is a very good book in my opinion. It is even more effective when you read it along with the courseware of the course by the same name.

*Foundations of Mathematical Logic* by Haskell B. Curry is a good book on this topic.

If you are interest in knowing it’s application in Computer Science then you can go for Discrete Mathematical Structures With Applications to Computer Science – Jean Paul Tremblay, Rampurkar Manohar .

- The shortest distance between any two distinct points is the line segment joining them.How can I see why this is true?
- Dividing the linear congruence equations
- Let $X$ and $Y$ be countable sets. Then $X\cup Y$ is countable
- When does $V/\operatorname{ker}(\phi)\simeq\phi(V)$ imply $V\simeq\operatorname{ker}(\phi)\oplus\phi(V)$?
- Why is there no “remainder” in multiplication
- $\frac{1}{{1 + {\left\| A \right\|} }} \le {\left\| {{{(I – A)}^{ – 1}}} \right\|}$
- Tangent bundle of $S^2$ not diffeomorphic to $S^2\times \mathbb{R}^2$
- Path connectedness is a topological invariant?
- $R$ is a commutative integral ring, $R$ is a principal ideal domain imply $R$ is a field
- What are the Laws of Rational Exponents?
- Can a function be increasing *at a point*?
- Rings with isomorphic proper subrings
- Prove that $\sqrt {n − 1} +\sqrt {n + 1}$ is irrational for every integer $n ≥ 1$
- Calculate Ellipse From Points?
- Proof that the sequence $s_n = \frac{1}{n}$ converges to $0$