## 104 Citations

### Bounded finite set theory

- MathematicsMath. Log. Q.
- 2021

We define an axiom schema IΔ0S for finite set theory with bounded induction on sets, analogous to the theory of bounded arithmetic, IΔ0 , and use some of its basic model theory to establish some…

### Neostability in countable homogeneous metric spaces

- MathematicsAnn. Pure Appl. Log.
- 2017

### Hereditarily Finite Sets in Constructive Type Theory

- Economics, MathematicsITP
- 2016

The axiomatization takes the empty set and adjunction as primitives and comes with a strong induction principle and the set operations of ZF are constructed and the basic theory of finite ordinals and cardinality is developed.

### Finitary Set Theory

- MathematicsNotre Dame J. Formal Log.
- 2009

The use of the adjunction operator (adding a single new element to an existing set) as a basis for building a finitary set theory allows a simplified axiomatization for the first-order theory of hereditarily finite sets and a rigorous characterization of the primitive recursive set functions.

### Addition and multiplication of sets

- MathematicsMath. Log. Q.
- 2007

The natural partial ordering associated with addition of sets is shown to be a tree, which allows us to prove that any set has a unique representation as a sum of additively irreducible sets and that the non-empty elements of any model of set theory can be partitioned into infinitely many submodels, each isomorphic to the original model.

### Cumulative hierarchies and computability over universes of sets

- Mathematics
- 2008

Various metamathematical investigations, beginning with Fraenkel’s historical proof of the independence of the axiom of choice, called for suitable deﬁnitions of hierarchical universes of sets. This…

### Executable Set Theory and Arithmetic Encodings in Prolog

- Computer ScienceArXiv
- 2008

A digraph representation of Hereditarily Finite Sets with Urelements is implemented and the surprising possibility of internally sharing isomorphic objects, independently of their language level types and meanings is uncovered.

### Ackermann encoding, bisimulations and OBDDs

- Computer ScienceTheory and Practice of Logic Programming
- 2004

An alternative way to represent graphs via OBDDs using the notion of Ackermann encoding of hereditarily finite sets into natural numbers is proposed and a method to compute at the same time the maximum bisimulation and the OBDD representation of a given graph is presented.

## References

SHOWING 1-2 OF 2 REFERENCES

### Untersuchungen über die Grundlagen der Mengenlehre. I

- Mathematics
- 1908

----------------------------------------------------Nutzungsbedingungen DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung…