Library 08


My name is Ali Sadegh Daghighi. I am a math Ph.D. from Amirkabir University of Technology in Iran working on set theory.

My Ph.D. dissertation has been completed in 2017 under supervision of Massoud Pourmahdian. I received my B.Sc. and M.Sc. degrees from Sharif University of Technology and Amirkabir University of Technology in pure mathematics and mathematical logic respectively. My M.Sc. thesis supervisor was also Massoud Pourmahdian.

My research in set theory is mainly concentrated on the interactions of large cardinals and forcing, tree property and non-well founded set theory. I am also interested in Shelah’s pcf theory and Woodin’s Ultimate L project.

More information about my research is available on my Academia and ResearchGate profiles as well as the Publications and Talks sections here in this website.

You can reach out to me via contact information available in the Contact page.


The list of my mathematical and non-mathematical interests is fairly long. In some of them I would like to become an expert and in some others I’m following the topic as a hobby and just out of curiosity. Here is a brief description of some of my interests:

  • Set Theory: As my primary research field and the foundation of mathematics which itself is the foundation of science, set theory is my main mathematical interest. Also studying the properties of infinite numbers as a kind of seemingly not that realistic creatures in comparison with other mathematical objects, shares many points with my philosophical interests and other non-mathematical areas of research. I’m particularly interested in very large cardinals, those which lie near the border of Kunen’s Inconsistency or even beyond it, namely various forms of Berkeley cardinals which are in contradiction with the Axiom of Choice.
  • Model Theory: It is deeply connected with set theory as well as being a rich and beautiful area of research and a useful tool in set theoretic constructions. So naturally model theory is a part of my mathematical interests, particularly categoricity theory and Abstract Elementary Classes.
  • Topology: I like this branch of mathematics because in topology extreme complexity grows out of pure simplicity! You begin from simplest possible notions on a very simple structure very close to pure sets, namely topological spaces, and then go forward to the realm of very hard and sometimes provably non-resolvable problems with a very simple formulation. It is also connected to logic through descriptive set theory and various model theoretic trends.
  • Astronomy: It is one of the branches of natural sciences that I’m really interested in. I hope to be one of those lucky people who will be an eyewitness of that forever memorable moment in which we, human beings, finally understand that we are not alone in the universe!
  • Philosophy: I believe that doing something without asking about its philosophy is like knowing how to do something without knowing why to do it! Consequently as a logician who works on the foundations of mathematics, it is a kind of necessity for me to know more about philosophy in general and philosophy of mathematics in particular. Maybe it is not too far-fetched if we say that no one could be a perfect logician without being interested in deep philosophical thoughts. Besides philosophy of mathematics, I’m also interested in epistemology, sociology and philosophy of mind, science and ethics.
  • History: Middle East is the most ancient part of the world and the origin of almost every important aspect of humanity. The first examples of the development of agriculture, scripts, cities, civilizations, kingdoms and empires, law and human rights, trading and money, mathematics, astronomy, science, architecture, arts, religions and wars, are all of a Middle Eastern origin. As an Iranian and a Middle Eastern who lives in a very ancient country full of important historical events which greatly influenced the existing human civilization and culture, archaeology and history is part of my interests simply because it is part of my identity. Naturally my special focus is on the interactions of Iranian ancient empires and other civilizations in and out of the region including Mesopotamia, Egypt, Greece and Roman empire. I’m also interested in scientific analysis of the origins of Middle Eastern religions particularly the historical interactions of ZoroastrianismMithraism, Manichaeism and Judaism and the influence of the combination of these different trends on early Christianity and Roman Empire.
  • Literature: As the son of a couple that consists from a theater dramatist and a literature fan who both were and are avid book collectors, I am the heir to a fairly large family library! It is not an exaggeration to say that I live among the books! I’m also an avid book collector and an amateur novelist myself. The picture in this post is inspired by Russell’s fascinating childhood adventure in the huge library of Pembroke Lodge, as it is described in the first chapter of Logicomix! Amazingly Russell’s life-time search for an absolute “truth” and a reliable “foundation” for human knowledge which led him to many wonderlands such as philosophy, science, mathematics and finally logic, is so similar to my journey through these kingdoms which is motivated by the same reason! However it will be a very long journey and I’m just in the first steps of this endless road! If you are curious to know what the books on the shelves are, here is a complete list. It is a good entertainment to find the special order that these collection of the books are ordered by! You don’t need the Axiom of Choice, though!
  • Linguistics: In some sense logic itself is a language and working via different logics is like speaking using different languages! On the other hand it seems people who speak in different languages think in different ways and via different logics! My great interest in the history and literature of the world unfolded the important role of the language in understanding different thought paradigms, life-styles and cultures to me. Based on this fact I have became interested in linguistics and etymology with a long term dream of becoming a polyglot. As someone who was born in Langarud city in Gilan province in north of Iran, besides Persian and English I know Gilaki as a native speaker as well as a bit Russian which is the primary or secondary language of the neighbor countries around the Caspian Sea. Also due to the Arabic language courses included in the education system in Iran, I could understand Arabic which itself made it easy for me to begin learning its sister languages, Aramaic and Hebrew, which are necessary for my studies in the history of Middle Eastern civilization. However I’m still far from becoming fluent in these languages. On the other hand I do plan to learn more about European sisters of Persian language namely German, Latin and Greek, particularly because of their significance in the European philosophy and literature as well as their key role in the etymology of Western branch of Indo-European languages. In this direction ancient Eastern Indo-European languages particularly Sanskrit and Avestan are also part of my etymological studies. A special project that I follow in my linguistic studies is to understand the interactions of the Middle Eastern languages of different roots particularly the situation of word exchanges between Persian and Hebrew languages. Such linguistic interactions are interesting because they indicate some historical interactions between people of different cultures.
  • Music: At last but not the least stands music which is my most favorited branch of arts. In short words, my taste of music is close to European classics, medieval folklore, non-vocal musics and everything that is close to my very classic definition of a beautiful song. Mozart, Vangelis and Secret Garden duo are among my favorite musicians and piano is my favorite music instrument. Just like Pythagoreans, I believe there is a hidden relation between mathematics as the most abstract knowledge and music as the most abstract art! Don’t you think that some special songs like Vangelis’ Conquest of Paradise and Carl Orff’s Fortuna have something to do with large cardinal theory?!


My Blog posts in this site are mainly about subjects that are related to my interests listed above. Thus you can find posts about almost every mathematical and non-mathematical subjects among them!

Please don’t forget to make comments and help me improve my knowledge in any of these vast areas of knowledge. You are welcome to add your feedback about the content and design of this site in the corresponding poll here.