I'm looking for a modern book on logic-set theory-foundation written as the Bourbaki's set theory. I'm particularly interested in a formal exposition of ZFC axiom with logic-set Grothendieck universe.
2026-04-01 05:40:08.1775022008
Modern reference on logic-set theory-foundation
663 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in REFERENCE-REQUEST
- Best book to study Lie group theory
- Alternative definition for characteristic foliation of a surface
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Random variables in integrals, how to analyze?
- Abstract Algebra Preparation
- Definition of matrix valued smooth function
- CLT for Martingales
- Almost locality of cubic spline interpolation
- Identify sequences from OEIS or the literature, or find examples of odd integers $n\geq 1$ satisfying these equations related to odd perfect numbers
- property of Lebesgue measure involving small intervals
Related Questions in LOGIC
- Theorems in MK would imply theorems in ZFC
- What is (mathematically) minimal computer architecture to run any software
- What formula proved in MK or Godel Incompleteness theorem
- Determine the truth value and validity of the propositions given
- Is this a commonly known paradox?
- Help with Propositional Logic Proof
- Symbol for assignment of a truth-value?
- Find the truth value of... empty set?
- Do I need the axiom of choice to prove this statement?
- Prove that any truth function $f$ can be represented by a formula $φ$ in cnf by negating a formula in dnf
Related Questions in SET-THEORY
- Theorems in MK would imply theorems in ZFC
- What formula proved in MK or Godel Incompleteness theorem
- Proving the schema of separation from replacement
- Understanding the Axiom of Replacement
- Ordinals and cardinals in ETCS set axiomatic
- Minimal model over forcing iteration
- How can I prove that the collection of all (class-)function from a proper class A to a class B is empty?
- max of limit cardinals smaller than a successor cardinal bigger than $\aleph_\omega$
- Canonical choice of many elements not contained in a set
- Non-standard axioms + ZF and rest of math
Related Questions in CATEGORY-THEORY
- (From Awodey)$\sf C \cong D$ be equivalent categories then $\sf C$ has binary products if and only if $\sf D$ does.
- Continuous functor for a Grothendieck topology
- Showing that initial object is also terminal in preadditive category
- Is $ X \to \mathrm{CH}^i (X) $ covariant or contravariant?
- What concept does a natural transformation between two functors between two monoids viewed as categories correspond to?
- Please explain Mac Lane notation on page 48
- How do you prove that category of representations of $G_m$ is equivalent to the category of finite dimensional graded vector spaces?
- Terminal object for Prin(X,G) (principal $G$-bundles)
- Show that a functor which preserves colimits has a right adjoint
- Show that a certain functor preserves colimits and finite limits by verifying it on the stalks of sheaves
Related Questions in FOUNDATIONS
- Difference between provability and truth of Goodstein's theorem
- Can all unprovable statements in a given mathematical theory be determined with the addition of a finite number of new axioms?
- Map = Tuple? Advantages and disadvantages
- Why doesn't the independence of the continuum hypothesis immediately imply that ZFC is unsatisfactory?
- Formally what is an unlabeled graph? I have no problem defining labeled graphs with set theory, but can't do the same here.
- Defining first order logic quantifiers without sets
- How to generalize the mechanism of subtraction, from naturals to negatives?
- Mathematical ideas that took long to define rigorously
- What elementary theorems depend on the Axiom of Infinity?
- Proving in Quine's New Foundations
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Bourbaki's book was idiosyncratic, and the terminology it used was never common. Contemporary books do not use terminology such as "assemblies"; they talk instead about "formulas" and "sentences".
The two most common contemporary books on set theory are Set Theory by Kunen and Set Theory (3rd edition) by Jech. Kunen's book is written in the style of a textbook, while Jech's is written in the style of a desk reference, but each book can serve both purposes. Both of these books start at the beginning and present set theory in a fully rigorous manner.
The existence of Grothendieck universes is equivalent to the existence of strongly inaccessible cardinals. Inaccessible cardinals are very well understood in set theory, so set theorists don't spend much time also talking about Grothendieck universes.