Do mathematicians who study Homotopy Type Theory think that it can be completely free from Godel-Rosser theorem?
2026-02-22 22:04:12.1771797852
Is HOTT, a new attempt at foundation of mathematics, free from incompleteness theorem or is it still suffering?
167 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ARITHMETIC
- Solve this arithmetic question without algebra
- Is division inherently the last operation when using fraction notation or is the order of operation always PEMDAS?
- Upper bound for recursion?
- Proving in different ways that $n^{n-1}-1$ is divisible by $(n-1)^2$.
- Meaning of a percentage of something
- Compare $2^{2016}$ and $10^{605}$ without a calculator
- The older you are, the richer you get?
- Easy question which doesn't make sense to me!
- Calculating diminishing interest amount
- Multiplication Question
Related Questions in HOMOTOPY-TYPE-THEORY
- What in general is a recursor?
- Homotopy Type Theory contradictions in definitions of propositions?
- Dependent type theory: universes may have a type?
- Define $\neg\neg A$ to be truncation using LEM
- Type former as primitive constants
- Primitive notions for positiv types
- How to Prove Homotopy Equivalence in a Discrete Topology
- Is HOTT, a new attempt at foundation of mathematics, free from incompleteness theorem or is it still suffering?
- Any path factor through the canonical lift uniquely
- Calculus in Homotopy Type Theory
Related Questions in UNIVALENT-FOUNDATIONS
- Define $\neg\neg A$ to be truncation using LEM
- Type former as primitive constants
- Can all mathematical operations be encoded with a Turing Complete language?
- Definition Of Equivalence
- Is HOTT, a new attempt at foundation of mathematics, free from incompleteness theorem or is it still suffering?
- Prospects of teaching/learning elementary math with computed-checked type theory
- Streicher's K axiom but for List
- Why can't you formulate Voevodsky's 2-theories in set theory if its the foundation of maths?
- Typos in HoTT appendix A.1.2?
- Path-Lifting in HoTT
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 goals of use HTT or variants thereof are to provide a better foundation than ZFC in a variety of respects such as being easier to work with in computer checked proofs. They don't intend to avoid Godel's theorems, and you cannot. If your system has a recursively enumeralable axiom list, is consistent, and can model Peano Arithmetic then Godel's theorems apply. Heck, you can get away with even weaker conditions: You can replace being able to model PA with just being able to model Robinson Arithmetic https://en.wikipedia.org/wiki/Robinson_arithmetic and the results still apply.