Question

Why is better to work with first-order logic than with second-order logic?

score 431 · Answer 1 · 2026-03-26 07:57:06

431

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Why is better to work with first-order logic than with second-order logic?

Published on 26 Mar 2026 - 7:57

score 2k · Answer 2 · 2026-03-26 11:18:28

2k

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Why is better to work with first-order Peano's axioms than with second-order Peano's axioms?

Published on 26 Mar 2026 - 11:18

score 146 · Answer 3 · 2014-02-25 01:30:26

146

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Not Skolem's Paradox - Part 3

Published on 25 Feb 2014 - 1:30

score 248 · Answer 4 · 2014-02-26 17:47:03

248

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Every Countable Model of PA is Recursive?

Published on 26 Feb 2014 - 17:47

score 293 · Answer 5 · 2014-02-27 03:01:12

293

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First-order Peano Axioms and order-completeness of $\mathbb{N}$

Published on 27 Feb 2014 - 3:01

score 306 · Answer 6 · 2026-03-25 17:26:22

306

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Hyperoperations and Peano's arithmetic ($\mathsf{PA}$)

Published on 25 Mar 2026 - 17:26

score 675 · Answer 7 · 2014-03-05 20:47:18

675

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Systems the Peano axioms can be derived in

Published on 05 Mar 2014 - 20:47

score 331 · Answer 8 · 2017-04-11 07:00:00

331

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Is an extension of a consistent theory that assumes its own finite consistency consistent?

Published on 11 Apr 2017 - 7:00

score 84 · Answer 9 · 2017-04-11 18:52:55

84

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How to prove that in the natural numbers "if $a = b$ then $a + c = b + d$ if and only if $c = d$" using Peano Axioms?

Published on 11 Apr 2017 - 18:52

score 641 · Answer 10 · 2026-03-28 00:27:47

641

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Is Peano arithmetic consistent in predicate logic? If so, what are the implications?

Published on 28 Mar 2026 - 0:27

score 820 · Answer 11 · 2017-04-13 06:11:10

820

Views

Proof of a proposition regarding recursive definitions (from Terence Tao's Analysis I)

Published on 13 Apr 2017 - 6:11

score 243 · Answer 12 · 2017-04-13 06:33:36

243

Views

How to prove $\text{Con}(PA + \text{Con}(PA))$ in $ZFC$?

Published on 13 Apr 2017 - 6:33

score 446 · Answer 13 · 2017-04-15 05:26:27

446

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Using Peano axioms to define natural numbers

Published on 15 Apr 2017 - 5:26

score 250 · Answer 14 · 2017-04-16 20:45:16

250

Views

Can you define an addition for natural numbers with the associativity property?

Published on 16 Apr 2017 - 20:45

score 132 · Answer 15 · 2017-04-17 03:18:28

132

Views

How to prove (if it is even needed) if $ac \leq bc$, then $a \leq b$ using Peano axioms

Published on 17 Apr 2017 - 3:18

List Question

Why is better to work with first-order logic than with second-order logic?

Why is better to work with first-order Peano's axioms than with second-order Peano's axioms?

Not Skolem's Paradox - Part 3

Every Countable Model of PA is Recursive?

First-order Peano Axioms and order-completeness of $\mathbb{N}$

Hyperoperations and Peano's arithmetic ($\mathsf{PA}$)

Systems the Peano axioms can be derived in

Is an extension of a consistent theory that assumes its own finite consistency consistent?

How to prove that in the natural numbers "if $a = b$ then $a + c = b + d$ if and only if $c = d$" using Peano Axioms?

Is Peano arithmetic consistent in predicate logic? If so, what are the implications?

Proof of a proposition regarding recursive definitions (from Terence Tao's Analysis I)

How to prove $\text{Con}(PA + \text{Con}(PA))$ in $ZFC$?

Using Peano axioms to define natural numbers

Can you define an addition for natural numbers with the associativity property?

How to prove (if it is even needed) if $ac \leq bc$, then $a \leq b$ using Peano axioms

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