Is it possible to prove $0 \neq 1$ in (non-univalent) Martin-Löf type theory, where $0$ and $1$ are natural numbers (defined using the usual inductive type $0 : \mathbb{N}$, $S : \mathbb{N} \to \mathbb{N}$)?
2026-03-30 03:05:33.1774839933
Disequality in Type Theory
73 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated 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 TYPE-THEORY
- Are Proofs of Dependent Pair Types Equivalent to Finding an Inverse Function?
- Types as formulas?
- Dependent vs. polymorphic types in modern type theories
- What in general is a recursor?
- 'Logically symmetric' expressions in lambda calculus
- (Higher order) logic/type theory/category theory like (meta-)grammar/language/machine?
- Cardinal collapse and (higher) toposes
- Does Diaconescu's theorem imply cubical type theory is non-constructive?
- Dependent type theory: universes may have a type?
- Define $\neg\neg A$ to be truncation using LEM
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?