# On long increasing chains modulo flat ideals

@article{Shelah2010OnLI, title={On long increasing chains modulo flat ideals}, author={Saharon Shelah}, journal={Mathematical Logic Quarterly}, year={2010}, volume={56} }

We prove that, e.g., in (ω 3)(ω 3) there is no sequence of length W4 increasing modulo the ideal of countable sets (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

## 8 Citations

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We deal with relatives of GCH which are provable. In particular, we deal with rank version of the revised GCH. Our motivation was to find such results when only weak versions of the axiom of choice…

Are all natural numbers the same.

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In these notes we present the method introduced by Neeman of generalized side conditions with two types of models. We then discuss some applications: the Friedman-Mitchell poset for adding a club in…

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We propose developing the theory of consequences of morasses relevant in mathematical applications in the language alternative to the usual one, replacing commonly used structures by families of sets…

LIST OF PUBLICATIONS

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1. Sh:a Saharon Shelah. Classification theory and the number of nonisomorphic models, volume 92 of Studies in Logic and the Foundations of Mathematics. North-Holland Publishing Co., Amsterdam-New…

## References

SHOWING 1-9 OF 9 REFERENCES

More on cardinal arithmetic

- MathematicsArch. Math. Log.
- 1993

This paper deals with variety of problems in pcf theory and infinitary combinatorics, looking at normal filters and prc, measures of the size of [lambda]^{ with |B_i|<mu_i, and the existence of strongly almost disjoint families.

Applications of PCF theory

- MathematicsJournal of Symbolic Logic
- 2000

Another version of exponentiation is characterized: maximal number of k-branches in a tree with λ nodes, and cardinal invariants for each λ with a pcf restriction are given.

The generalized continuum hypothesis revisited

- Mathematics
- 1998

We can reformulate the generalized continuum problem as: for regular κ<λ we have λ to the power κ is λ, We argue that the reasonable reformulation of the generalized continuum hypothesis, considering…

Archive for mathematical logic

- Philosophy
- 1987

The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or…

THE JOURNAL OF SYMBOLIC LOGIC

- Philosophy
- 2000

‘Fuzzy logic’ means different things to different people. For some it is a philosophy of life – “a way to break the stranglehold that the black-and-white thinking of the Western tradition has upon…

Israel Journal of Mathematics

- 116:285–321,
- 2000

Sh 410] Saharon Shelah. More on Cardinal Arithmetic. Archive for Mathematical Logic

- Sh 410] Saharon Shelah. More on Cardinal Arithmetic. Archive for Mathematical Logic
- 1993

Set theory Springer Monographs in Mathematics The third millennium edition, revised and expanded

- Set theory Springer Monographs in Mathematics The third millennium edition, revised and expanded
- 2003

Springer-Verlag

- Berlin,
- 2003