foundational work in mathematics
C3329
concept
Foundational work in mathematics comprises the theories, principles, and formal systems that rigorously define mathematical objects and reasoning, providing a secure logical basis for all mathematical disciplines.
All labels observed (15)
| Label | Occurrences |
|---|---|
| foundational system for mathematics | 3 |
| foundational framework for mathematics | 2 |
| foundational work in algebraic geometry | 2 |
| foundational work in mathematics canonical | 2 |
| principle in the philosophy of mathematics | 2 |
| foundational concept in calculus | 1 |
| foundational program in mathematics | 1 |
| foundational system for arithmetic | 1 |
| foundational system for constructive mathematics | 1 |
| foundational text in geometry | 1 |
| foundational theory of mathematics | 1 |
| foundational work in the philosophy of mathematics | 1 |
| foundations of mathematics program | 1 |
| mathematical foundational stance | 1 |
| mathematics foundation | 1 |
Instances (21)
| Instance | Via concept surface |
|---|---|
| Kronecker’s finitism | mathematical foundational stance |
| Basic Law V | principle in the philosophy of mathematics |
| Hume’s Principle (derivable, not postulated) | principle in the philosophy of mathematics |
| Martin-Löf type theory | foundational system for constructive mathematics |
| homotopy type theory | foundational framework for mathematics |
| epsilon–delta definition of limit | foundational concept in calculus |
| Zermelo–Fraenkel set theory | foundational system for mathematics |
| Frege’s system in "Grundgesetze der Arithmetik" | foundational system for arithmetic |
| Principia Mathematica | — |
| GAGA (Géométrie Algébrique et Géométrie Analytique) | foundational work in algebraic geometry |
|
EGA
surface form:
Éléments de Géométrie Algébrique
|
foundational work in algebraic geometry |
| naive set theory | foundational theory of mathematics |
| Hilbert’s program | foundational program in mathematics |
| Sadleirian foundation | mathematics foundation |
| Über die Hypothesen, welche der Geometrie zu Grunde liegen | foundational text in geometry |
| Elements | — |
| Grundlagen der Mathematik | foundational work in the philosophy of mathematics |
| Isabelle/ZF | foundational framework for mathematics |
| univalent foundations program | foundations of mathematics program |
| Morse–Kelley set theory by class–set distinction | foundational system for mathematics |
|
calculus of constructions
surface form:
Calculus of Constructions
|
foundational system for mathematics |