Email:
golshani.m
''at'' gmail.com

Post-Doctoral Research Fellow,

School of Mathematics, Institute for Research in Fundamental Sciences (IPM).

The effects of adding a real to models of set theory**.**

1-
Shelah's strong
covering property and CH in V[r]*,**
*with E. Eslami,* **Math. Log. Q.* 58
(2012), no. 3, 153–158.

2-
Independence of higher Kurepa hypotheses,
*with Sy D. Friedman,
Arch. Math. Logic*
51 (2012), no. 5-6, 621–633.

3-
Almost Souslin Kurepa trees,
*Proc. Amer. Math. Soc. 141 (2013), no. 5, 1821-1826.*

4- Killing the GCH everywhere with a single real, with Sy D. Friedman, J. Symbolic Logic 78 (2013), no 3, 803-823.

5- Killing GCH everywhere by a cofinality-preserving forcing notion over a model of GCH, with Sy D. Friedman, Fund. Math. 223 (2013), no 2, 171-193.

6- The foundation axiom and elementary self-embeddings of the universe, with A. S. Daghighi, J. D. Hamkins, and E. Jeřábek, in: Infinity, Computability, and Metamathematics: Festschrift celebrating the 60th birthdays of Peter Koepke and Philip Welch (S. Geschke, B. Löwe, and P. Schlicht, eds.), College Publications, London, 2014, pp. 89–112.

7-
More on almost Souslin Kurepa trees,
*Proc. Amer. Math. Soc. 142 (2014), no 10, 3631-3634.*

*8-
Adding a lot of Cohen reals by adding a few I, with M. Gitik, Trans.
**Amer. Math. Soc. 367 (2015), no. 1, 209-229.*

9- Adding a lot of Cohen reals by adding a few II, with M. Gitik, Fund. Math. 231 (2015), 209-224.

10- Collapsing the cardinals of HOD, with J. Cummings and Sy D. Friedman, J. Math. logic.15 (2015), no. 2, 1550007, 32 pp.

11- On Foreman's maximality principle, with Y. Hayut, J. Symbolic Logic. 81 (2016), no 4, 1344-1356.

12- On cuts in ultraproducts of linear orders I, with S. Shelah, J. Math. Log. 16 (2016), no. 2, 1650008, 34 pp.

13- HOD, V and the GCH, J. Symbolic Logic. 82 (2017), no. 1, 224–246.

14- An Easton like theorem in the presence of Shelah cardinals, Arch. Math. Logic 56 (2017), no. 3-4, 273–287.

15-
A Groszek-Laver pair of undistinguishable E_{0}
classes, with V. Kanovei and V. Lyubetsky, *
Math. Log. Q.* 63 (2017), no. 1-2, 19-31.

16- The tree property on a countable segment of successors of singular cardinals, with Y. Hayut, Fund. Math. 240 (2018), no 2, 199-204.

17- The tree property at double successors of singular cardinals of uncountable cofinality, with R. Mohammadpour, Ann. Pure Appl. Logic 169 (2018), no. 2, 164–175.

18-
The
tree property at the successor of a singular limit of measurable cardinals,
* Arch. Math. Logic 57 (2018), no. 1-2, 3-25.*

19-
On a
question of Silver about gap-two cardinal transfer principles, with Sh. Mohsenipour,
*Arch. Math. Logic 57 (2018), no. 1-2, *
27-35.

20- Adding a lot of random reals by adding a few, with M. Gitik, Fund. Math. 241 (2018), no 1, 97-108.

21- On cuts in ultraproducts of linear orders II, with S. Shelah, accepted for J. Symbolic Logic.

22- Definable tree property can hold at all uncountable regular cardinals, submitted.

23- Special Aronszajn tree property, with Y. Hayut, submitted.

24- (Weak) diamond can fail at the least inaccessible cardinal, submitted.

25- Tree property at all regular even cardinals, submitted.

26- Specializing trees and answer to a question of Williams, with S. Shelah, submitted.

27-
On
C^{s}_{n}(κ) and the Juhasz-Kunen question, with S. Shelah,
submitted.

28- The generalized Kurepa hypothesis at singular cardinals, submitted.

Papers in preparation

1- On slow minimal reals and r.e. degrees, with S. Shelah.

2- On a question of Hamkins and Löwe on the modal logic of collapse forcing, with W. Mitchell.

3- The tree property at \aleph_{\omega+2} with an infinite gap, with Sy D. Friedman, R. Honzik and S. Stejskalova.

4- Adding many fresh subsets to singular cardinals, with M. Gitik.

5- Regularity properties of Cohen and random reals, with W. Brian.

6- GCH can fail everywhere in a definable way, with Sy D. Friedman.

Notes

2- An introduction to forcing.

3- Singular cofinality conjecture and a question of Gorelic.

5- Power set at \aleph_\omega: On a theorem of Woodin.

6- All uncountable regular cardinals can be inaccessible in HOD.

7- Notes on countably generated complete Boolean algebras.

8- Adding many random reals may add many Cohen reals.

10- On the notions of cut, dimension and transcendence degree for models of ZFC.

Students

1- Rahman Mohammadpour, MSc: ``The Modal Logic of Forcing and Hamkins' Maximality Principle'' (in Farsi), 2015.

2- Zahra A. Biglou, MSc: ``Around Vaught's conjecture'' (in Farsi), 2018.