U+22A9 "⊩" Forces Unicode Character
Unicode Version 17.0
⊩
U+22A9 "⊩" Forces is a mathematical symbol used in logic and formal semantics, particularly in the context of modal logic and possible world semantics, to represent the forcing relation. It is most famously employed in forcing theory, a technique in set theory developed by Paul Cohen to prove independence results, such as the independence of the Continuum Hypothesis from Zermelo-Fraenkel set theory. In this setting, the symbol "⊩" denotes that a certain condition forces a particular statement to be true in a generic extension of a model of set theory, making it a critical notation for expressing relationships between partially ordered sets and logical formulas.
General Properties
| Code Point | U+22A9 |
| Version Added | 1.1 |
| Name | Forces |
| Block | Mathematical Operators |
| General Category | Math Symbol |
| Canonical Combining Class | Not Reordered |
| Bidirectional Class | Other Neutral |
| Mirrored | Yes |
| Mirrored Character | "⫣" U+2AE3 Double Vertical Bar Left Turnstile |
Encodings
| HTML Decimal Encoding | ⊩ |
| HTML Hex Encoding | ⊩ |
| UTF-8 Encoding | 0xE2 0x8A 0xA9 |
| UTF-16 Encoding | 0x22A9 |
| UTF-32 Encoding | 0x000022A9 |
| C/C++/Java Escape | \u22a9 |
Unicode Properties
| NFC Quick Check | Yes |
| NFD Quick Check | Yes |
| NFKC Quick Check | Yes |
| NFKD Quick Check | Yes |
| Numeric Type | None |
| Numeric Value | NaN |
| Line Break | Alphabetic |
| Script | Common |
| Script Extensions | Common |
| Indic Syllabic Category | Other |
| Pattern Syntax | Yes |
| Math | Yes |
| Vertical Orientation | Rotated |
| Grapheme Base | Yes |
| Grapheme Cluster Break | Other |
| Word Break | Other |
| Sentence Break | Other |