# In Praise of Replacement

@article{Kanamori2012InPO, title={In Praise of Replacement}, author={Akihiro Kanamori}, journal={The Bulletin of Symbolic Logic}, year={2012}, volume={18}, pages={46 - 90} }

Abstract This article serves to present a large mathematical perspective and historical basis for the Axiom of Replacement as well as to affirm its importance as a central axiom of modern set theory.

## 16 Citations

The Hierarchy of Sets

- Economics
- 2014

This chapter introduces a set theory that interprets and is interpretable in the theory of lists from Chaps. 3 and 4.

Mathias and set theory

- MathematicsMath. Log. Q.
- 2016

On the occasion of his 70th birthday, the work of Adrian Mathias in set theory is surveyed in its full range and extent.

Implicit dynamic function introduction and its connections to the foundations of mathematics

- Computer Science
- 2012

Two formalisms are sketched, both extensions of Dynamic Predicate Logic, that innovatively do capture this feature of the natural language of mathematics and that differ only in the limitations they impose onto it.

Rigor and Structure

- Geology, Psychology
- 2015

Preface Acknowledgments 1. Rigor and Rigorization 2. Rigor and Foundations 3. Structure and Structuralism 4. Structure and Foundations Bibliography

Frege, Dedekind, and the Origins of Logicism

- Philosophy
- 2013

This paper has a two-fold objective: to provide a balanced, multi-faceted account of the origins of logicism; to rehabilitate Richard Dedekind as a main logicist. Logicism should be seen as more…

Mathematical Limits and Philosophical Significance of Transfinite Computation

- Mathematics
- 2014

Author(s): Rin, Benjamin | Advisor(s): Barrett, Jeffrey A; Walsh, Sean | Abstract: The general aim of this thesis is to explore applications of transfinite computation within the philosophy of…

Transfinite recursion and computation in the iterative conception of set

- PhilosophySynthese
- 2014

This paper considers several kinds of recursion principles and proves results concerning their relation to one another, and considers philosophical motivations for these formal principles coming from the idea that computational notions lie at the core of the conception of set.

Set Theory: A First Course

- Mathematics
- 2016

Set theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly…

The Assets-Claims on Assets Equivalence in the Axiomatic Method

- Economics
- 2016

The purpose of the study is to analyze the assets-claims on assets equivalence based on the dual concept of monetary units and the axiomatic method. The methodology is analytical, rationalistic and…

Gödel vis-à-vis Russell: Logic and set Theory to Philosophy

- PhilosophyKurt Gödel Philosopher-Scientist
- 2016

Godel’s work from the beginning to his first substantive explorations in philosophy would to a significant extent be contextualized by, reactive to, and reflective of, Russell’s. Russell was the…

## References

SHOWING 1-10 OF 178 REFERENCES

Transfinite numbers

- History
- 1997

In a series of revolutionary articles written during the last quarter of the nineteenth century, the great German mathematician Georg Cantor removed the age-old mistrust of infinity and created an…

The philosophy of mathematics today

- Philosophy
- 1998

PART I: ONTOLOGY, MODELS, AND INDETERMINACY PART II: MATHEMATICS, SCIENCE, AND METHOD PART III: FINITISM AND INTUITIONISM PART IV: FREGE AND THE FOUNDATIONS OF ARITHMETIC PART V: SETS, STRUCTURE, AND…

A note on the schemes of replacement and collection

- MathematicsArch. Math. Log.
- 2007

The schemes of are derived from certain weak forms of the same that are related to the schemes of by analogy with the following:.

What Does it Take to Prove Fermat's Last Theorem? Grothendieck and the Logic of Number Theory

- MathematicsThe Bulletin of Symbolic Logic
- 2010

The set theoretic assumptions used in the current published proof of Fermat's Last Theorem are explored, how these assumptions figure in the methods Wiles uses, and the currently known prospects for a proof using weaker assumptions.

Logical dilemmas - the life and work of Kurt Gödel

- Art
- 1996

Kurt Goedel's seminal achievements that changed the perception and foundations of mathematics are explained in the context of his life from the turn of the century Austria to the Institute for Advanced Study in Princeton.

Cantorian set theory and limitation of size

- Philosophy
- 1984

Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on…

A provisional solution to the normal Moore space problem

- Mathematics
- 1980

The Product Measure Extension Axiom (PMEA), whose consistency would follow from the existence of a strongly compact cardinal, implies that every normalized collection of sets in a space of character…

Unordered pairs in the set theory of Bourbaki 1949

- Mathematics
- 2010

Working informally in ZF, we build a pair of supertransitive models of Z, of which pair the union is shown to be a supertransitive model of Bourbaki’s 1949 system for set theory in which some…