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 E0 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, J. Symbolic Logic. 83 (2018), no 1, 29-39.
22- The generalized Kurepa hypothesis at singular cardinals, Period. Math. Hungar. 78 (2019), no. 2, 200–202.
23- The Special Aronszajn tree property, with Y. Hayut, J. Math. Log. 20 (2020), no. 1, 2050003, 26 pp.
24- The tree property at double successors of singular cardinals of uncountable cofinality with infinite gaps, with A. Poveda, Ann. Pure Appl. Logic 172 (2021), no. 1, 102853.
25- Specializing trees and answer to a question of Williams, with S. Shelah, J. Math. Log. 21 (2021), no. 1, 2050023, 20 pp.
26- (Weak) diamond can fail at the least inaccessible cardinal, Fund. Math. 256 (2022) , no 2, 113-129.
27- The Keisler-Shelah isomorphism theorem and the continuum hypothesis, with S. Shelah, Fund. Math. accepted.
28- Definable tree property can hold at all uncountable regular cardinals,
29- The tree property at all regular even cardinals,
30- The special Aronszajn tree property at \aleph_2 and GCH, with D. Aspero.
31- On a question of Hamkins and Lowe on the modal logic of collapse forcing, with W. Mitchell.
32- On slow minimal reals I, with S. Shelah.
33- Combinatorial and number-theoretic properties of generic reals, with W. Brian.
34- Shelah's partition functions and the Hales-Jewett numbers, with M. Mirabi.
35- Kaplansky test problems for R-modules in ZFC, with M. Asgharzadeh and S. Shelah.
36- NNR revisited, with S. Shelah.
37- Usuba's principle UB_\lambda can fail at singular cardinals, with S. Shelah.
38- On Csn(κ) and the Juhasz-Kunen question, with S. Shelah.
39- Completeness of the Godel-Lob provability logic for the filter sequence of normal measures, with R. Zoghifard.
40- Graphs represented by Ext, with M. Asgharzadeh and S. Shelah.
41- The Keisler-Shelah isomorphism theorem and the continuum hypothesis II, with S. Shelah.
42- Representing the language of a topos as quotient of the category of spans, with A.R Shir Ali Nasab.
43- On the sequence (pcf^\alpha (A) : \alpha in Ord).
44- No universal graphs at uncountable regular cardinals.
1- Woodin's surgery method.
2- An introduction to forcing.
3- Singular cofinality conjecture and a question of Gorelic.
4- On a question of Zadrozny.
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.
9- On a theorem of Magidor.
10- On the notions of cut, dimension and transcendence degree for models of ZFC.
11- Fraisse limit via forcing.
12- Changing measurable into small accessible cardinals.
13- Strongly compct diagonal Prikry forcing.
14- Two remarks on Merimovich's model of the total failure of GCH
15- Cardinal collapsing and product forcing, with R. Mohammadpour.
1- Singular Cardinals Problem (IPM Colloquium, 2015).
2- On the birth of set theoretic algebra (Algebra day, 2018).
3- Diophantine approximation of Cohen reals (7th annual conference of Iranian Association for Logic, 2020).
4- Completeness of the provability logic GL with respect to the filter sequence of normal measures (8th annual conference of Iranian Association for Logic, 2021).
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.
3- Zakieh Zakeri, MSc: ``Topics in Cardinal Arithmetic'' (in Farsi), 2020.