What is the proof-theoric ordinal of Lawvere's elementary theory of the category of sets?
2026-03-25 01:26:16.1774401976
Proof-theoric ordinal of ETCS
125 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
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 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 ORDINALS
- Ordinals and cardinals in ETCS set axiomatic
- For each cardinal number $u$, there exists a smallest ordinal number $\alpha$ such that card$\alpha$ =$u$ .
- Intuition regarding: $\kappa^{+}=|\{\kappa\leq\alpha\lt \kappa^{+}\}|$
- Set membership as a relation on a particular set
- Goodstein's sequences and theorem.
- A proof of the simple pressing down lemma, is sup $x=x?$
- $COF(\lambda)$ is stationary in $k$, where $\lambda < k$ is regular.
- Difficulty in understanding cantor normal form
- What are $L_1$ and $L_2$ in the Gödel Constructible Hierarchy
- How many subsets are produced? (a transfinite induction argument)
Related Questions in PROOF-THEORY
- Decision procedure in Presburger arithmetic
- Is this proof correct? (Proof Theory)
- Finite axiomatizability of theories in infinitary logic?
- Stochastic proof variance
- If $(x^{(n)})^∞_{n=m}$ is Cauchy and if some subsequence of $(x^{(n)})^∞_{n=m}$ converges then so does $(x^{(n)})^∞_{n=m}$
- Deduction in polynomial calculus.
- Are there automated proof search algorithms for extended Frege systems?
- Exotic schemes of implications, examples
- Is there any formal problem that cannot be proven using mathematical induction?
- Proofs using theorems instead of axioms
Related Questions in ORDINAL-ANALYSIS
- Is there a "solution" to the ordinal game?
- How do we know PA is incomparable with PRA + $\epsilon_0$?
- Modifying the "base" of Veblen's hierarchy to exceed $\Gamma_0$
- Does there exist a notion of "growth rate", big-O notation, etc for ordinal (normal) functions?
- What is the lowest layer of the Constructible Universe which is a model of $ZFC-P$?
- Question on An Explicit Enumeration of Ordinals
- What is the proof-theoretic ordinal of $ \mathsf{PA}+\mathsf{TI}(\prec_{\varepsilon_0})$?
- At which ordinal this "counting" ordinal language would fail?
- Proof-theoric ordinal of ETCS
- Infinite ordinals in proof theory
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?
The current state-of-the-art for proof-theoretic ordinals is somewhere around $\Pi^1_2$-CA$_0$, a subtheory of second-order arithmetic Z$_2$ which in turn is much weaker than ETCS. So at present this is extremely open.